Question

Length of resonance tube is 150 cm how many resonance are possible for a wave having frequency 400 hertz and speed of sound is 320 metre per second

Answer 1

Answer: 4 Resonance possible.

Explanation:

λ= Velocity/Frequency

=320/400

=80 cm

First resonating structure at λ/4 =20cm.

Second resonating structure at 3λ/4 = 60cm

Third =90

Fourth= 120

Resonance does not take place at 150, as it is boundary.

Answer 2

The possible resonance for wave will be 3.

Explanation:

Given that,

Frequency = 400 hertz

Sound velocity = 320 m/s

Length of tube = 150 cm

We need to calculate the wavelength

Using formula of wavelength

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

Put the value into the formula

$\lambda=\dfrac{320}{400}$

$\lambda=0.8\ m$

$\lamda=80\ cm$

We need to calculate the number of resonance

Using formula of number of resonance

For one loop,

$L=\dfrac{\lambda}{2}$

$L=\dfrac{80}{2}=40\ cm$

For second loop,

$L=\dfrac{\lambda}{2}$

$L=\dfrac{2\times80}{2}=80\ cm$

For third loop,

$L=\dfrac{\lambda}{2}$

$L=\dfrac{3\times80}{2}=120\ cm$

For fourth loop,

$L=\dfrac{\lambda}{2}$

$L=\dfrac{4\times80}{2}=160\ cm$

Here, the length of the tube is 150 cm so neglect of the fourth loop.

Hence, The possible resonance for wave will be 3.

Learn more :

Topic ; number of resonance

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