Question 450: Waves

Question

An obstacle is moving towards the source with velocity $$v$$. The sound is reflected from the obstacle. If $$c$$ is the speed of sound and $$\lambda$$ is the wavelength, then the wavelength of the reflected wave $$\lambda_r$$ is

Accepted Answer

When an obstacle moves towards a sound source, the sound waves reflect off the obstacle. To find the wavelength of the reflected wave, denoted as $\lambda_r$, we start by considering the changes in frequency due to the movement of the obstacle.
Step-by-Step Explanation
Frequency of the Reflected Sound Wave:
The frequency $ f_r $ of the reflected sound wave when the obstacle is moving towards the source can be determined by the formula:
$    f_r = f \left(\frac{c+v}{c-v}\right)    $
Here, $ c $ is the speed of sound, $ v $ is the velocity of the obstacle, and $ f $ is the original frequency of the sound wave.
No Change in Velocity:
The velocity of the sound wave remains unchanged, even after it is reflected. This means the speed of sound $ c $ is constant before and after reflection.
Wavelength of the Reflected Wave:
Since the velocity is unchanged and frequency changes, it affects the wavelength. Using the relationship between speed, frequency, and wavelength:
$    \frac{c}{\lambda_T} = \frac{c}{\lambda} \left(\frac{c+v}{c-v}\right)    $
Simplifying this equation gives the wavelength of the reflected wave, $\lambda_T$, as:
$    \lambda_T = \left(\frac{c-v}{c+v}\right) \lambda    $
This equation describes how the wavelength of the sound wave changes upon reflection from a moving obstacle.
Thus, the wavelength of the reflected wave $\lambda_r$ is given by:
$ \lambda_T = \left(\frac{c-v}{c+v}\right) \lambda $

Answer

$$\lambda_r=\left(\frac{c-v}{c+v}\right) \lambda$$

Answer

$$\lambda_r=\left(\frac{c+v}{c-v}\right) \lambda$$

Answer

$$\lambda_r=\left(\frac{c-v}{c}\right) \lambda$$

Answer

$$\lambda_r=\left(\frac{c+v}{c}\right) \lambda$$

Waves

An obstacle is moving towards the source with velocity $v. The sound is reflected from the obstacle. If c is the speed of sound and \lambda is the wavelength, then the wavelength of the reflected wave \lambda_r$ is

Choose the correct answer: