Physics · Chapter 9
Study notes aligned to the official NEB syllabus.
Acoustics is the branch of physics that deals with the production, transmission, and reception of sound. Sound is a longitudinal mechanical wave: it needs a material medium (solid, liquid, or gas) to travel and cannot propagate through a vacuum. The particles of the medium vibrate back and forth along the same direction in which the wave travels, creating regions of compression (high pressure) and rarefaction (low pressure).
The basic wave relation for sound of speed $v$, frequency $f$, and wavelength $\lambda$ is:
$$v = f\lambda$$
This chapter focuses on the Doppler effect (the apparent change in frequency due to relative motion between source and observer), the idea of pressure amplitude, the intensity of sound, and the characteristics of musical sound.
The Doppler effect is the apparent change in the frequency (and hence pitch) of sound heard by an observer when there is relative motion between the source of sound and the observer.
Key idea: the actual frequency emitted by the source does not change. What changes is the frequency received by the observer, because relative motion alters either the wavelength of the waves reaching the observer or the speed of the waves relative to the observer, or both.
Symbols used throughout:
The apparent frequency in every case is found from:
$$f' = \frac{v'}{\lambda'}$$
where $v'$ is the speed of the sound waves relative to the observer and $\lambda'$ is the wavelength of the waves actually reaching the observer.
When the source moves, it "chases" or "runs away from" the waves it emits, so the wavelength in front of and behind it is changed, while the wave speed relative to the stationary observer stays $v$.
The source moves towards the observer with speed $u_s$ (observer speed $u_o = 0$). In one time period the source moves closer, so the waves ahead are crowded together and the apparent wavelength shortens to:
$$\lambda' = \frac{v - u_s}{f}$$
Therefore the apparent frequency is:
$$ \begin{aligned} f' &= \frac{v'}{\lambda'} \ &= \frac{v}{\lambda'} \ &= \left(\frac{v}{v - u_s}\right) f \end{aligned} $$
Since $v - u_s < v$, we get $f' > f$.
Conclusion: the apparent frequency increases when the source of sound moves towards the stationary observer (the pitch rises).
The source recedes from the observer with speed $u_s$ ($u_o = 0$). Now the waves behind the source are stretched out, so the apparent wavelength lengthens to:
$$\lambda' = \frac{v + u_s}{f}$$
Therefore:
$$f' = \left(\frac{v}{v + u_s}\right) f$$
Since $v + u_s > v$, we get $f' < f$.
Conclusion: the apparent frequency decreases when the source of sound moves away from the stationary observer (the pitch falls).
When only the observer moves, the wavelength of the waves in the medium is unchanged, but the speed of the waves relative to the observer changes.
The observer moves towards the source with speed $u_o$ (source speed $u_s = 0$). The observer runs into the waves, so the relative wave speed becomes $v' = v + u_o$, while the wavelength stays $\lambda = v/f$:
$$ \begin{aligned} f' &= \frac{v'}{\lambda} \ &= \frac{v + u_o}{v/f} \ &= \left(\frac{v + u_o}{v}\right) f \end{aligned} $$
Since $v + u_o > v$, we get $f' > f$.
Conclusion: the apparent frequency increases when the observer moves towards the stationary source.
The observer moves away from the source with speed $u_o$ ($u_s = 0$). The observer moves with the waves, so fewer reach the ear per second and the relative wave speed becomes $v' = v - u_o$:
$$f' = \left(\frac{v - u_o}{v}\right) f$$
Since $v - u_o < v$, we get $f' < f$.
Conclusion: the apparent frequency decreases when the observer moves away from the stationary source.
Acoustics is the branch of physics that deals with the production, transmission, and reception of sound. Sound is a longitudinal mechanical wave: it needs a material medium (solid, liquid, or gas) to travel and cannot propagate through a vacuum. The particles of the medium vibrate back and forth along the same direction in which the wave travels, creating regions of compression (high pressure) and rarefaction (low pressure).
The basic wave relation for sound of speed , frequency , and wavelength is:
This chapter focuses on the Doppler effect (the apparent change in frequency due to relative motion between source and observer), the idea of pressure amplitude, the intensity of sound, and the characteristics of musical sound.
The Doppler effect is the apparent change in the frequency (and hence pitch) of sound heard by an observer when there is relative motion between the source of sound and the observer.
Key idea: the actual frequency emitted by the source does not change. What changes is the frequency received by the observer, because relative motion alters either the wavelength of the waves reaching the observer or the speed of the waves relative to the observer, or both.
Symbols used throughout:
The apparent frequency in every case is found from:
where is the speed of the sound waves relative to the observer and is the wavelength of the waves actually reaching the observer.
When the source moves, it "chases" or "runs away from" the waves it emits, so the wavelength in front of and behind it is changed, while the wave speed relative to the stationary observer stays .
The source moves towards the observer with speed (observer speed ). In one time period the source moves closer, so the waves ahead are crowded together and the apparent wavelength shortens to:
Therefore the apparent frequency is:
Since , we get .
Conclusion: the apparent frequency increases when the source of sound moves towards the stationary observer (the pitch rises).
The source recedes from the observer with speed (). Now the waves behind the source are stretched out, so the apparent wavelength lengthens to:
Therefore:
Since , we get .
Conclusion: the apparent frequency decreases when the source of sound moves away from the stationary observer (the pitch falls).
When only the observer moves, the wavelength of the waves in the medium is unchanged, but the speed of the waves relative to the observer changes.
The observer moves towards the source with speed (source speed ). The observer runs into the waves, so the relative wave speed becomes , while the wavelength stays :
Since , we get .
Conclusion: the apparent frequency increases when the observer moves towards the stationary source.
The observer moves away from the source with speed (). The observer moves with the waves, so fewer reach the ear per second and the relative wave speed becomes :
Since , we get .
Conclusion: the apparent frequency decreases when the observer moves away from the stationary source.