Question

Is the phase difference between two points is 120° for a
wave with velocity of 360 m/s and frequency 500 Hz,
then path difference between the two points is-
a) 24 cm​

Answer 1

Answer:

Path difference = 24 cm

Explanation:

Given:

• Phase difference = 120°
• Velocity of the wave = 360 m/s
• Frequency = 500 hz

To Find:

• The path difference

Solution:

First finding the wavelength of the wave.

We know that,

$\boxed{\tt \lambda=\dfrac{v}{\nu} }$

where λ is the wavelength, v is the velocity and ν is the frequency of the given wave.

Substituting the data we get,

$\tt \lambda=\dfrac{360}{500}$

$\tt \lambda = 0.72\:m$

Hence the wavelength of the given wave is 0.72 m.

Now finding the path difference between the two points which is given by the equation,

$\boxed{\tt \phi=\dfrac{2\: \pi}{\lambda} \times path\:difference}$

where φ = phase difference, λ is the wavelength of the wave

Substituting the data,

$\tt 120=\dfrac{2\: \pi}{0.72} \times path\:difference$

$\tt 2\: \pi \times Path\:difference=86.4$

$\tt Path\:difference=\dfrac{43.2}{\pi}$

$\implies \tt 0.24\:m=24\:cm$

Hence the path difference of the waves is 24 cm.

Answer 2

Question:-

• Is the phase difference between two points is 120° for a wave with velocity of 360 m/s and frequency 500 Hz,then path difference between the two points is

To Find:-

• Find the path difference.

Given:-

• Velocity of wave is 360m/s

• Phase difference is 120°

• Frequency is 500 hz

Solution:-

First ,

We have to find the wave length:-

$\longrightarrow\sf \: Wave length = \cancel\dfrac { 360 } { 500 }$

$\longrightarrow\sf \: 0.72 m$

Then ,

We have to find the path difference:-

$\longrightarrow\sf \: 120 = \dfrac { 2 π } { 0.72 } \times Path$

$\longrightarrow\sf \: Path \: Difference\dfrac { 43.2 } { π }$

$\longrightarrow\sf \: 24 \: cm$

Hence ,

• Path difference is 24 cm