Question

Figure shows a tube having sound source at one end and observer at other end. Source produces frequencies upto 10000 Hz. Speed of sound is 400 m/s. Find the frequencies at which person hears maximum intensity :

Answer 1

The sound waves will travel straight and it will divide at right angle and start travelling straight and then again meet at the other end.

first wave which will go straight travels 10 cm and the wave which goes through a longer distance travels 30 cm

therefore the path difference $\Delta p=P_2-P_1=30-10=20cm$

for constructive interference to occur at the point near to the person $\Delta p=n\lambda$

$\lambda =\frac{v}{f}$

$\Delta p=n\frac{v}{f}$

$f=n\frac{v}{\Delta p}=\frac{400n}{20\times {10}^{-2}}=2000n$

frequencies within the specified range

for n = 1 f=2000Hz

for n = 2 f = 4000Hz

for n = 3 f = 6000Hz

for n = 4 f = 8000Hz

for n = 5 f = 10000Hz