A vehicle, with a horn of frequency n is moving with a velocity of 30 m/s in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency $n+n_1$. Then (if the sound velocity in air is 300 m/s)

Question

A steel wire with mass per unit length $ 7.0 \times 10^{-3} \, \text{kg/m} $ is under a tension of $ 70 \, \text{N} $. The speed of transverse waves in the wire will be:

Answer 1

To solve this problem, we need to understand the Doppler effect and how it applies when an observer and a source are in relative motion. In this scenario, the vehicle is moving in a direction perpendicular to the line joining the observer and the vehicle. This means there is no component of the vehicle’s velocity toward or away from the observer.

The Doppler effect formula relating the observed frequency $ f' $ when the source or observer moves, is given by:

f' = \left( \frac{v + v_o}{v + v_s} \right) f

Where:

v is the speed of sound in the medium (300 m/s in this case).
v_o is the velocity of the observer (0 m/s here, as the observer is stationary).
v_s is the velocity of the source (the vehicle, 30 m/s), but since it moves perpendicular, this velocity does not affect the Doppler shift in frequency.
f is the original frequency of the source.
f' is the observed frequency.

Given the observer perceives frequency as n + n_1, we equate:

f' = n + n_1

However, since the velocity of the vehicle is perpendicular, it does not contribute to a frequency change. Thus, the frequency heard by the observer remains the same as that emitted by the source.

Therefore, n_1 = 0, meaning no change in frequency is perceived by the observer. This eliminates the Doppler effect possibility in perpendicular motion.

Thus, the correct answer is n_1=0.

Answer 2