Velocity of sound in air is 300 m/s. Then the distance between two successive nodes of a stationary wave of frequency 1000 Hz is.a)20cmb)15 cmc)30cmd)10 cmCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

The distance between two successive nodes in a stationary wave can be determined using the formula:

$d = \frac{v}{2f}$

where:
- $d$ is the distance between two successive nodes
- $v$ is the velocity of sound in air
- $f$ is the frequency of the wave

In this case, we are given that the velocity of sound in air is 300 m/s and the frequency of the wave is 1000 Hz. Let's substitute these values into the formula to find the distance between two successive nodes.

Calculation:
$d = \frac{300}{2 \times 1000}$
$d = \frac{300}{2000}$
$d = 0.15$ m

Thus, the distance between two successive nodes is 0.15 m.

Converting the distance to centimeters:
$0.15 \, \text{m} = 0.15 \times 100 \, \text{cm}$
$= 15 \, \text{cm}$

Therefore, the correct answer is option B) 15 cm.

Answer

Velocity of sound in air= 300m/s =300×100=30000 cm/s
And frequency = 1000 hz
So, wavelength = Velocity/frequency
= 30000/1000= 30
Distance = wavelength/2
=30/2 = 15

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