Question

A man marries a great Wagnerism soprano but alas, he discovers he can stand wagnerian opera. In order to save his eardrums, the unhappy man decides he must silence his lark-like wife for good. His plan is to tie her to the front of his car and send car and soprano speeding towards a brick wall. This soprano, however is quite shrewd, having studies physics in her student days at the music conservatory. she realized that this wall has a resonant frequency of 600 Hz. That is the wall will fall down if a continuous sound waves of 600 Hz hit it, and she will be saved to sing again. The car is heading towards the wall at 30 m$s^{-1}$. At what frequency must the soprano sing so that the wall will crumble?
($V=330m{s}^{-1}$)

• A. 545.45 Hz
• B. 550.2 Hz
• C. 560 Hz
• D. 565.3 Hz

Answer 1

The correct option is A 545.45 Hz

Say frequency must the soprano sign is $\nu$, resonance freq is given which is ${\nu }^{\prime }=600Hz$, $V=330m{s}^{-1}$ and $v_s=30m{s}^{-1}$ are the velocity of sound in the air and velocity of the car towards wall respectively.

Then we apply Dopler's effect in sound wave:

${\nu }^{\prime }=\frac{V}{V-v_s}\nu$

$\nu =\frac{V-v_s}{V}{\nu }^{\prime }=\frac{330-30}{330}\times 600Hz=\frac{6000}{11}=545.45Hz$