Lesson Notes By Weeks and Term v3 - Senior Secondary 2
Sound waves
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Sound waves
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: Physics
Class: Senior Secondary 2
Term: 1st Term
Week: 7
Theme: Waves-Motion Without Material Transfer
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Students should beable to:L. identify the vibrating sourceswhen souris-is produced. distinguishbetween:Noise and music.In tensity and loudness.pitch and rrequency CSappl.ed to sound. explain for cedvibration and explain how it is used to amplify as ound. use the relationship V=fx in solving numerical problems. Explain the formation of standing waves and produce the se.waves In stretchingstrings. Use resonance tubeto determine the veloc.tv of sound in air.
Waves-Motion Without Material Transfer is the end correction (a small distance beyond the open end where the antinode actually forms). At the second resonance, the air column forms a three-quarter-wavelength standing wave: $L_2 = \frac{3\lambda}{4} - e$.
Subtracting the two equations: $L_2 - L_1 = \left(\frac{3\lambda}{4} - e\right) - \left(\frac{\lambda}{4} - e\right) = \frac{2\lambda}{4} = \frac{\lambda}{2}$.
Therefore, $\lambda = 2(L_2 - L_1)$. Once the wavelength ($\lambda$) is determined, the speed of sound (V) can be calculated using the formula: $V = f\lambda$, where 'f' is the known frequency of the tuning fork. Alternatively, from the first resonance $L_1 + e = \lambda/4$, so $\lambda = 4(L_1+e)$. The end correction 'e' can be approximated as $0.3D$, where D is the diameter of the tube. Or, $e = \frac{L_2 - 3L_1}{2}$.
Note: The speed of sound depends on temperature. For more accurate results, the speed measured at room temperature (Vt) can be related to the speed at 0°C (Vo) by $V_t = V_0 \sqrt{1 + \frac{T}{273}}$, where T is the temperature in °C. Approximately, $V_t = 331 + 0.6T$ (m/s).
3. Teaching and Learning Activities 3.1 Introduction (10 minutes)
Teacher Activity: Begins by asking students to describe different sounds they hear daily (e.g., from vehicles, market, school bell). Prompts them to consider how these sounds are produced. Teacher introduces the topic "Sound Waves." Student Activity: Students share examples of sounds and initial thoughts on their production. 3.2 Activity 1: Identifying Vibrating Sources (15 minutes)
Teacher Activity: Demonstrates sound production: Plucks a guitar string or 'goje' string, strikes a tuning fork, taps a drum, speaks. Guides students to touch the vibrating objects (e.g., a vibrating tuning fork against a finger, a loudspeaker cone). Asks students to identify the part of the object that is vibrating when sound is produced. Leads a discussion on common vibrating sources in the environment (e.g., vocal cords, engine parts, wind instruments).
Student Activity: Students observe demonstrations. Carefully touch vibrating objects to feel the vibration. Actively participate in identifying vibrating sources and providing examples. 3.3 Activity 2: Distinguishing Noise and Music (15 minutes)
Teacher Activity: Plays short audio clips: one of a musical piece (e.g., traditional Nigerian music, a classical piece) and another of noise (e.g., traffic jam, construction site, discordant sounds). Asks students to describe their feelings or reactions to each sound. Leads a discussion on the characteristics that make one sound pleasant (music) and the other unpleasant (noise). Formally defines and explains the differences.
Student Activity: Students listen to the audio clips. Describe their subjective experience of each sound. Contribute to the discussion, identifying characteristics like rhythm, harmony, regularity for music, and irregularity, harshness for noise. 3.4 Activity 3: Understanding Intensity/Loudness and Pitch/Frequency (20 minutes)
Teacher Activity: Uses a guitar or 'goje' (or a simple vibrator): Plucks a string gently (low amplitude) and then forcefully (high amplitude). Asks students to compare the perceived "strength" of the sound. Explains intensity and loudness, connecting amplitude to intensity. Uses the same instrument or a different one (e.g., a flute and a 'gangan' drum): Produces a high-pitched sound and a low-pitched sound. Asks students to describe the difference. Explains pitch and frequency, connecting frequency to pitch. Clarifies the subjective vs. objective nature of these pairs.
Student Activity: Observe the demonstrations. Describe the differences in sound strength and perceived highness/lowness. Engage in Q&A to consolidate understanding. 3.5 Activity 4: Forced Vibration and Resonance Demonstration (20 minutes)
Teacher Activity: Demonstrates forced vibration: Strikes a tuning fork and holds it in the air (sound is faint). Then holds the vibrating tuning fork against a wooden table or a resonance box. Students observe the increase in loudness. Explains that the table/box is forced to vibrate, and when the frequency matches, resonance occurs, amplifying the sound. If available, demonstrate two tuning forks of the same frequency – strike one and hold it near the other (if on resonance boxes), the second might start vibrating (sympathetic vibration, a form of resonance).
Student Activity: Sound waves Term: 1st Term Week: 14 ---
1. Overview and Learning Objectives This topic introduces students to the fundamental properties and characteristics of sound waves. Sound is an integral part of the human experience and plays a crucial role in communication, entertainment, and various technological applications within Nigeria and globally. Understanding sound waves provides a foundation for appreciating musical instruments, architectural acoustics, and even the functioning of biological hearing systems. Upon completion of this lesson, students will be able to: Identify the sources of vibration responsible for producing sound. Differentiate between noise and music. Distinguish between intensity and loudness, and between pitch and frequency, as applied to sound. Explain the phenomenon of forced vibration and describe its application in sound amplification. Apply the wave equation (V=fλ) to solve numerical problems related to sound waves. Explain the formation of standing waves and demonstrate their production using stretched strings. Conduct an experiment using a resonance tube to determine the velocity of sound in air.
2. Key Concepts and Explanations 2.1 Production of Sound: Vibrating Sources Sound is produced by vibrations. When an object vibrates, it causes the air particles around it to vibrate, creating compressions (regions of high pressure) and rarefactions (regions of low pressure) that propagate as a longitudinal wave through a medium.
Vibration: A rapid to-and-fro or oscillatory motion of an object about a fixed position.
Examples of vibrating sources: Human vocal cords: Vibrate when air passes over them during speech or singing.
Musical instruments: Strings: Guitar, violin, 'goje', 'sasa' (stringed instrument) strings vibrate when plucked or bowed.
Air columns: Flute, trumpet, 'algaita' (wind instrument) produce sound by vibrating columns of air.
Membranes: Talking drum ('iya ilu'), 'gangan', tambourine skins vibrate when struck.
Plates/Bars: Cymbals, xylophone bars vibrate when struck.
Bells: Vibrate when struck.
Loudspeakers: Diaphragm vibrates in response to electrical signals. 2.2 Distinction between Noise and Music Both noise and music are forms of sound, but they differ in their characteristics and perception.
Music: Produced by regular, periodic, and harmonious vibrations. Pleasing to the ear, characterized by rhythm, melody, and harmony. Has definite pitch and clear overtones.
Examples: Sounds from a well-played 'kora', 'talking drum' ensemble, symphony orchestra.
Noise: Produced by irregular, non-periodic, and discordant vibrations. Unpleasant or jarring to the ear, often perceived as irritating. Lacks definite pitch and clear overtones; a jumble of frequencies.
Examples: Traffic sounds in Lagos, sounds from a jackhammer, random shouting, the sound of a falling object. 2.3 Intensity vs. Loudness These terms are often used interchangeably in everyday language, but in physics, they have distinct meanings.
Sound Intensity (I): Defined as the amount of sound energy passing per unit time through a unit area perpendicular to the direction of propagation. It is an objective, measurable physical quantity. Mathematically, $I = \frac{P}{A}$, where $P$ is the power (energy per unit time) and $A$ is the area.
Unit: Watts per square metre (W/m2). Intensity is proportional to the square of the amplitude of the sound wave ($I \propto A^2$).
Factors affecting intensity: Amplitude of vibration, distance from source, density of the medium.
Loudness: A subjective physiological sensation in the listener's ear, related to how strong or weak a sound is perceived. It depends on the intensity of the sound, but also on the sensitivity of the ear and the frequency of the sound. There is no direct unit for loudness, but the perceived loudness level is measured in decibels (dB), which relates to intensity logarithmically. A sound of higher intensity is generally perceived as louder, but the relationship is not linear. For instance, doubling the intensity does not necessarily double the perceived loudness. 2.4 Pitch vs. Frequency These terms describe different aspects of sound perception and physical properties.
Frequency (f): An objective, measurable physical quantity. Defined as the number of complete oscillations or cycles of a sound wave that pass a point per unit time. * Unit: Hertz (Hz), where 1 Hz = is measured in decibels (dB), which relates to intensity logarithmically. A sound of higher intensity is generally perceived as louder, but the relationship is not linear. For instance, doubling the intensity does not necessarily double the perceived loudness. 2.4 Pitch vs. Frequency These terms describe different aspects of sound perception and physical properties.
Frequency (f): An objective, measurable physical quantity. Defined as the number of complete oscillations or cycles of a sound wave that pass a point per unit time.
Unit: Hertz (Hz), where 1 Hz = 1 cycle per second. Determines the pitch of a sound.
Human hearing range: Approximately 20 Hz to 20,000 Hz.
Pitch: A subjective physiological sensation related to how high or low a sound is perceived. Primarily determined by the frequency of the sound wave. A higher frequency corresponds to a higher pitch, and a lower frequency corresponds to a lower pitch.
Example: A child's voice typically has a higher pitch (higher frequency) than an adult male's voice. The sound of a flute has a higher pitch than a bass drum. 2.5 Forced Vibration and Resonance These are important phenomena in understanding how sound is amplified and produced in many instruments.
Forced Vibration: Occurs when an oscillating system (the driven system) is made to vibrate by an external force at the frequency of that external force (the driving frequency). The driven system vibrates at the frequency of the driving force, not necessarily its own natural frequency.
Example: If a vibrating tuning fork is held against a tabletop, the tabletop will be forced to vibrate at the frequency of the tuning fork. The vibrations of the tabletop are usually of larger amplitude and louder than the tuning fork alone because the tabletop has a larger surface area to push more air.
Resonance: A special case of forced vibration where the driving frequency of the external force matches the natural frequency (or one of the natural frequencies) of the oscillating system. When resonance occurs, the amplitude of the vibrations of the driven system increases significantly, leading to a much louder sound or larger displacement.
How it is used to amplify sound: Musical Instruments: Many instruments like guitars, violins, and 'talking drums' have hollow bodies or soundboxes. The vibrating strings or membranes force the air inside the soundbox to vibrate. If the frequency of the vibrating string/membrane matches a natural frequency of the air column or the body of the instrument, resonance occurs, amplifying the sound produced.
Tuning Forks: A tuning fork placed on a resonance box (open-ended wooden box) will cause the air column inside the box to resonate, producing a much louder sound than the tuning fork alone.
Microphones: Designed to resonate at specific frequencies to pick up sound efficiently. 2.6 The Relationship V=fλ This is the fundamental wave equation that relates the velocity, frequency, and wavelength of any wave, including sound waves. V = fλ V: Velocity (speed) of the wave (metres per second, m/s). It depends on the medium through which the wave travels (e.g., speed of sound in air is approximately 330-340 m/s at room temperature; in water, it's about 1500 m/s; in steel, about 5000 m/s). f: Frequency of the wave (Hertz, Hz). λ (lambda): Wavelength of the wave (metres, m). It is the distance between two consecutive compressions or rarefactions (or any two corresponding points) of a wave. Worked
Example: A siren emits sound with a frequency of 400 Hz. If the speed of sound in air is 330 m/s, calculate the wavelength of the sound wave.
Given: Frequency, f = 400 Hz Velocity, V = 330 m/s Formula: V = fλ Rearrange to find λ: λ = V / f Calculation: λ = 330 m/s / 400 Hz = 0.825 m Answer: The wavelength of the sound wave is 0.825 meters. 2.7 Formation of Standing Waves in Stretching Strings Standing waves (or stationary waves) are formed when two waves of the same frequency, amplitude, and speed travelling in
A siren emits sound with a frequency of 400 Hz. If the speed of sound in air is 330 m/s, calculate the wavelength of the sound wave.
Given:
Frequency, f = 400 Hz
Velocity, V = 330 m/s
Formula: V = fλ
Rearrange to find λ: λ = V / f
Calculation: λ = 330 m/s / 400 Hz = 0.825 m
Answer: The wavelength of the sound wave is 0.825 meters.
2.7 Formation of Standing Waves in Stretching Strings
Standing waves (or stationary waves) are formed when two waves of the same frequency, amplitude, and speed travelling in opposite directions superpose (interfere). In a stretched string, this occurs when an incident wave travels along the string and reflects off a fixed end, interfering with the continuously generated incident waves.
Characteristics:
Nodes: Points on the string that remain stationary (zero amplitude of vibration). These are regions of destructive interference. The fixed ends of a string are always nodes.
Antinodes: Points on the string where the amplitude of vibration is maximum. These are regions of constructive interference.
The energy in a standing wave is localized; it does not propagate along the string.
Production in stretching strings:
When a string (e.g., on a 'goje' or guitar) is plucked, struck, or bowed, it vibrates.
If the frequency of vibration is just right, the reflected waves interfere constructively and destructively to form a stable pattern of nodes and antinodes.
Fundamental Frequency (First Harmonic): The simplest standing wave pattern, with nodes at both ends and one antinode in the middle. The length of the string (L) is equal to half a wavelength ($\frac{\lambda_1}{2}$). So, $\lambda_1 = 2L$.
First Overtone (Second Harmonic): Nodes at both ends and one in the middle, with two antinodes. The length of the string (L) is equal to one full wavelength ($\lambda_2$). So, $\lambda_2 = L$.
Second Overtone (Third Harmonic): Nodes at both ends and two in between, with three antinodes. The length of the string (L) is equal to one and a half wavelengths ($\frac{3\lambda_3}{2}$). So, $\lambda_3 = \frac{2L}{3}$.
The frequencies of these harmonics are integer multiples of the fundamental frequency ($f_1, 2f_1, 3f_1$, etc.).
2.8 Using Resonance Tube to Determine the Velocity of Sound in Air
A resonance tube experiment utilizes the principle of resonance in an air column to determine the speed of sound.
Apparatus: A long glass tube, a water reservoir/beaker, a tuning fork of known frequency, a rubber hammer, a metre rule, and a thermometer.
Principle: When a vibrating tuning fork is held over the open end of a resonance tube, the air column inside the tube will resonate (amplify the sound) if its length is an odd multiple of a quarter wavelength of the sound produced by the tuning fork.
Procedure:
Adjust the water level in the glass tube so that the air column is very short.
Strike a tuning fork (e.g., 512 Hz) with a rubber hammer and hold it over the open end of the tube.
Slowly lower the water level (increasing the length of the air column) while continuously vibrating the tuning fork.
Listen for the loudest sound (first resonance point). Measure the length of the air column ($L_1$) from the open end to the water surface using the metre rule.
Continue lowering the water level until a second loud sound (second resonance point) is heard. Measure this length ($L_2$).
Record the ambient temperature using a thermometer.
Calculations:
At the first resonance, the air column forms a quarter-wavelength standing wave: $L_1 = \frac{\lambda}{4} - e$, where 'e' is the end correction (a small distance beyond the open end where the antinode actually forms).
At the second resonance, the air column forms a three-quarter-wavelength standing wave: $L_2 = \frac{3\lambda}{4} - e$.
Subtracting the two equations: $L_2 - L_1 = \left(\frac{3\lambda}{4} - e\right) - \left(\frac{\lambda}{4} - e\right) = \frac{2\lambda}{4} = \frac{\lambda}{2}$.
Therefore, $\lambda = 2(L_2 - L_1)$.
Once the wavelength ($\lambda$) is determined, the speed of sound (V) can be calculated using the formula: $V = f\lambda$, where 'f' is the known frequency of the tuning fork.
Alternatively, from the first resonance $L_1 + e = \lambda/4$, so $\lambda = 4(L_1+e)$. The end correction 'e' can be approximated as $0.3D$, where D is the diameter of the tube. Or, $e = \frac{L_2 - 3L_1}{2}$.
Note:* The speed of sound depends on temperature. For more accurate results, the speed measured at room temperature (Vt) can be related to the speed at 0°C (Vo) by $V_t = V_0 \sqrt{1 + \frac{T}{273}}$, where T is the temperature in °C. Approximately, $V_t = 331 + 0.6T$ (m/s).
Teaching and Learning Activities
3.1 Introduction (10 minutes)