A stationary source sends back and forth monochromatic sound. A w: app...
Analysis:
To analyze the change in wavelength of sound after reflection from a wall, we can use the Doppler effect formula. The Doppler effect describes the change in frequency (and therefore wavelength) of a wave due to the relative motion between the source and observer. In this case, the source is stationary and the observer is moving towards the source.
Given:
- Velocity of the observer (v) = 33 cm/s
- Propagation velocity of sound in the medium (v₀) = 330 m/s
Using the Doppler effect formula for sound:
The formula for the apparent frequency (f') observed by the moving observer is given by:
f' = (v₀ + v) / (v₀) * f
where f is the frequency of the source.
Frequency and Wavelength Relationship:
The frequency (f) and wavelength (λ) of a wave are inversely proportional. They are related by the equation:
v = f * λ
where v is the velocity of the wave.
Change in Wavelength:
To determine the change in wavelength after reflection, we need to compare the wavelengths before and after reflection. Since the source is stationary, the frequency of the sound remains the same.
Let's analyze the options:
(a) The wavelength of sound decreases: This is incorrect because the observer is approaching the stationary source, causing an increase in the apparent frequency. According to the frequency-wavelength relationship, an increase in frequency corresponds to a decrease in wavelength. Thus, the wavelength of the sound should increase, not decrease.
(b) The wavelength of sound increases: This is correct because as the observer moves towards the stationary source, the apparent frequency increases. According to the frequency-wavelength relationship, an increase in frequency corresponds to an increase in wavelength. Therefore, the wavelength of the sound should increase after reflection from the wall.
(c) Change in wavelength is 1%: This cannot be determined without knowing the original wavelength of the sound. The change in wavelength depends on the relative velocities of the observer and the source, and cannot be determined solely from the given information.
(d) Change in wavelength is 0.1%: This cannot be determined without knowing the original wavelength of the sound. The change in wavelength depends on the relative velocities of the observer and the source, and cannot be determined solely from the given information.
Conclusion:
The correct answer is (b) The wavelength of sound increases after reflection from the wall. The change in wavelength cannot be determined from the given information.