In a kundt`s tube ,stationary waves of frequency 1000Hz are produced .if the distance between 6 successive nodes is 82.5cm ,the speed of sound in the gas filled in the tube is1)300m/s2)330m/s3)360m/s4)390m/s

To determine the speed of sound in the gas filled in a Kundt's tube, we can use the relationship between frequency, wavelength, and wave speed. The formula we need is:

Wave Speed Formula

The speed of a wave (v) is given by the equation:

v = f × λ

where:

• v is the speed of sound in the medium (in meters per second, m/s),
• f is the frequency of the wave (in hertz, Hz),
• λ is the wavelength (in meters, m).

Finding the Wavelength

In this case, we know the frequency (f = 1000 Hz) and the distance between 6 successive nodes (82.5 cm). To find the wavelength, we first need to understand how nodes are spaced in a standing wave pattern.

In a standing wave, the distance between two successive nodes is half of the wavelength. Therefore, if the distance between 6 nodes is 82.5 cm, we can calculate the distance between one node and the next:

Calculating the Distance Between Nodes

The distance between 6 nodes includes 5 segments (since the first node is at the start and the last node is at the end). Thus:

Distance between 6 nodes = 5 × (distance between two nodes)

Let d be the distance between two successive nodes:

5d = 82.5 cm

Now, converting 82.5 cm to meters gives us:

5d = 0.825 m

Now, solving for d:

d = 0.825 m / 5 = 0.165 m

Finding the Wavelength

Since the distance between two nodes is half the wavelength:

λ = 2d = 2 × 0.165 m = 0.33 m

Calculating the Speed of Sound

Now that we have both the frequency and the wavelength, we can find the speed of sound:

v = f × λ = 1000 Hz × 0.33 m = 330 m/s

Final Answer

Thus, the speed of sound in the gas filled in the tube is 330 m/s, which corresponds to option 2) 330 m/s.