Question
A standing wave is formed between two loudspeakers that emit sound waves of frequency f.
A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is \(1.5 \mathrm{~m}\). The speed of sound is \(300 \mathrm{~m} \mathrm{~s}^{-1}\).
What is \(f\) ?
A. \(400 \mathrm{~Hz}\)
B. \(200 \mathrm{~Hz}\)
C. \(100 \mathrm{~Hz}\)
D. \(50 \mathrm{~Hz}\)
▶️Answer/Explanation
Ans:C
In a standing wave, the distance between consecutive maxima (or minima) is half of the wavelength (\(\lambda/2\)). Given that the distance between two consecutive sound maxima is \(1.5 \, \text{m}\), we can find the wavelength (\(\lambda\)):
\(\lambda/2 = 1.5 \, \text{m}\)
\(\lambda = 2 \cdot 1.5 \, \text{m} = 3 \, \text{m}\)
Now, we can use the formula for the speed of a wave:
\[v = f \cdot \lambda\]
Let’s solve for \(f\):
\[300 \, \text{m/s} = f \cdot 3 \, \text{m}\]
Now, divide both sides by 3:
\[f = \frac{300 \, \text{m/s}}{3 \, \text{m}} = 100 \, \text{Hz}\]
So, the frequency (\(f\)) of the sound waves is \(100 \, \text{Hz}\).
Light of wavelength λ0 is emitted from a nearby galaxy. The light is received on Earth and the wavelength is measured to be λ where λ<λ0. Which of the following correctly describes the speed and direction of motion of the galaxy?
Answer/Explanation
Markscheme
A
Examiners report
The vast majority of candidates understood that the fractional change in the wavelength was needed and hence discounted B or D. But it would seem that they did not read the stem carefully, where it is clear that the wavelength has decreased – indicating that it is travelling towards Earth.
A fire engine with its siren sounding approaches and passes a stationary observer. The frequency of the sound emitted by the siren is \({f_s}\). The frequency of the sound measured by the observer is \({f_o}\). Which of the following describes the relationship between \({f_o}\) and \({f_s}\)?
Answer/Explanation
Answer – A
If the observer moves toward the stationary source,
The observed frequency is higher than the source frequency. If the observer is moving away from the stationary source, the observed frequency is lower than the source frequency
An ambulance emits a sound of frequency f as it travels along a straight road between stationary observers A and B.
Which of the following shows how the frequency of the sound heard by each observer compares with f?
Answer/Explanation
Answer – C
For observer B ambulance is approaching towards him so fobs is greater then f.
If the observer moves toward the stationary source,
The observed frequency is higher than the source frequency
And for observer A source is moving away from him so fobs is lesser then f
If the observer is moving away from the stationary source, the observed frequency is lower than the source frequency
A point source of sound is moving to the right at constant speed. The source emits sound waves of constant frequency. The speed of the source is less than the speed of sound. Which diagram correctly shows the wavefronts of the sound?
Answer/Explanation
Answer – A
Towards right wavelength gets compressed and towards left wavelength gets expanded