Question

On a quiet day, when a whistle crosses you then its pitch decreases in the ratio 4/5. If the temperature on that day is 20${}^o$C, then the speed of whistle will be ____ (given the velocity of sound at 0${}^{o}C$ = 332 m/s)

• A. 28.2 m/s
• B. 38.2 m/s
• C. 18.2 m/s
• D. 48.2 m/s

Answer 1

The correct option is B 38.2 m/s

pitch of sound is directly proportional to the frequency and frequency is directly proportional to the velocity of the sound .

relation between temperature and velocity of sound in air

$\frac{V_T}{V_0}=\sqrt{\frac{T}{T_0}}$

$\frac{V_T}{V_0}=\sqrt{\frac{293}{273}}=1.035$

$V_T=343.62$ m/s

applying doppler effect

when whistle is approaching observer $\frac{f_a}{f_0}=\frac{V_T}{V_T-V_W}$

when whistle is distancing from observor $\frac{f_d}{f_0}=\frac{V_T}{V_T+V_W}$

dividing these two equations we have ,

$\frac{f_d}{f_a}=\frac{V_T-V_W}{V_T+V_W}=\frac{4}{5}$

$V_W=\frac{V_T}{9}$

$V_W=38.2$m/s

so answer is B.