Question

Question:Kundt’s method for measuring the speed of sound. In Fig. 17-51, a rodRis clamped at its center; a diskDat its end projects into a glass tube that has cork filings spread over its interior. A plungerPis provided at the other end of the tube, and the tube is filled with a gas. The rod is made to oscillate longitudinally at frequencyfto produce sound waves inside the gas, and the location of the plunger is adjusted until a standing sound wave pattern is set up inside the tube. Once the standing wave is set up, the motion of the gas molecules causes the cork filings to collect in a pattern of ridges at the displacement nodes $f=4.46\times {10}^3$. and the separation between ridges is 9.20 cm, what is the speed of sound in the gas?

Short answer

The speed of sound in the gas is$821\frac{m}{s}$

Step-by-step solution

The given data 

• i)The frequency of sound wave is$f=4.46\times {10}^{3}Hz$
• ii) The distance between two ridges is$d=9.20cmor0.092m$

Understanding the concept of the interference of the standing waves

Use the concept of interference and standing waves and can find the wavelength from the distance between two ridges. The equation of speed-related to the frequency and wavelength of a wave will give us the speed of sound in the gas.

Formula:

The speed of a standing wave,$V=\lambda f$ (i)

Calculation of speed of sound in the gas

Given that the ridges are formed at the nodes of standing waves. So, the distance between ridges will represent the distance of half wavelength.

Hence, the wavelength of sound waves inside Kundt’s tube is
$\lambda =2\times d$
= 0.184m

Using equation (i), the speed of sound waves inside the tube can be given as:
$$\begin{gathered} V=0.184\times 4.46\times {10}^3 \\ =820.64 \\ ~821\frac{m}{s} \end{gathered}$$

Hence, the value of the speed of the sound waves is$821\frac{m}{s}$