$A$ train,standing in a station yard,blows a whistle of frequency $400 \, Hz$ in still air. The wind starts blowing in the direction from the yard to the station with a speed of $10 \, m/s$. Given that the speed of sound in still air is $340 \, m/s$. Mark the $INCORRECT$ statement:

  • A
    The frequency of sound as heard by an observer standing on the platform is $400 \, Hz$.
  • B
    The speed of sound for the observer standing on the platform is $350 \, m/s$.
  • C
    The frequency of sound as heard by the observer standing on the platform will increase.
  • D
    The wavelength of sound as received by the observer standing on the platform will increase.

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The speed of sound in mercury at a certain temperature is $1450 \, m/s$. Given the density of mercury as $13.6 \times 10^3 \, kg/m^3$,the bulk modulus for mercury is:

The ratio of the speed of sound in helium gas to that in nitrogen gas at the same temperature is $\left(\gamma_{He}=\frac{5}{3}, \gamma_{N_2}=\frac{7}{5}, M_{He}=4, M_{N_2}=28\right)$

$A$ steel rod $100 \; cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53 \; kHz$. What is the speed (in $km/s$) of sound in steel?

The speed of sound in air:

Assume that the displacement $(s)$ of air is proportional to the pressure difference $(\Delta p)$ created by a sound wave. Displacement $(s)$ further depends on the speed of sound $(v)$,density of air $(\rho)$,and the frequency $(f)$. If $\Delta p \approx 10 \, Pa$,$v \approx 300 \, m/s$,$\rho \approx 1 \, kg/m^3$,and $f \approx 1000 \, Hz$,then $s$ will be of the order of (take multiplicative constant to be $1$).

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