Ask question

Ask question

All categories

3 years ago

11

A policeman in a stationary car measures the speed of approaching cars by means of an ultrasonic device that emits a sound with

a frequency of 41.2 khz. A car is approaching him at a speed of 33.0 m/s. The wave is reflected by the car and interferes with the emitted sound producing beats. What is the frequency of the beats? The speed of sound in air is 330 m/s.

2 answers:

beks73 [17]3 years ago

6 0

Answer:

4.6 kHz

Explanation:

The formula for the Doppler effect allows us to find the frequency of the reflected wave:

$f'=(\frac{v}{v-v_s})f$

where

f is the original frequency of the sound

v is the speed of sound

vs is the speed of the wave source

In this problem, we have

f = 41.2 kHz

v = 330 m/s

vs = 33.0 m/s

Therefore, if we substitute in the equation we find the frequency of the reflected wave:

$f'=(\frac{330 m/s}{330 m/s-33.0 m/s})(41.2 kHz)=45.8 kHz$

And the frequency of the beats is equal to the difference between the frequency of the reflected wave and the original frequency:

$f_B = |f'-f|=|45.8 kHz-41.2 kHz|=4.6 kHz$

lara [203]3 years ago

6 0

The frequency of the beats is about 9.2 kHz

$\texttt{ }$

<h3>Further explanation</h3>

Let's recall the Doppler Effect formula as follows:

$\large {\boxed {f' = \frac{v + v_o}{v - v_s} f}}$

<em>f' = observed frequency</em>

<em>f = actual frequency</em>

<em>v = speed of sound waves</em>

<em>v_o = velocity of the observer</em>

<em>v_s = velocity of the source</em>

<em>Let's tackle the problem!</em>

$\texttt{ }$

<u>Given:</u>

actual frequency = f = 41.2 kHz

velocity of the car = v_c = 33.0 m/s

speed of sound in air = v = 330 m/s

<u>Asked:</u>

frequency of the beats = Δf = ?

<u>Solution:</u>

<em>Firstly , we will use the formula of </em><em>Doppler Effect</em><em> as follows:</em>

$f' = \frac{v + v_c}{v - v_c} \times f$

$f' = \frac{330 + 33}{330 - 33} \times 41.2$

$f' = \frac{363}{297} \times 41.2$

$f' = \frac{11}{9} \times 41.2$

$f' = 50 \frac{16}{45} \texttt{ kHz}$

$f' \approx 50.4 \texttt{ kHz}$

$\texttt{ }$

<em>Next , we could calculate the frequency of the beats as follows:</em>

$\Delta f = f' - f$

$\Delta f \approx 50.4 - 41.2$

$\Delta f \approx 9.2 \texttt{ kHz}$

$\texttt{ }$

<h3>Conclusion:</h3>

The frequency of the beats is about 9.2 kHz

$\texttt{ }$

<h3>Learn more</h3>

Doppler Effect : brainly.com/question/3841958
Example of Doppler Effect : brainly.com/question/810552

$\texttt{ }$

<h3>Answer details</h3>

Grade: College

Subject: Physics

Chapter: Sound Waves

$\texttt{ }$

Keywords: Sound, Wave , Wavelength , Doppler , Effect , Policeman , Stationary , Frequency , Speed , Beats

You might be interested in

Jeremy stands on the edge of a cliff. He throws three identical rocks with the same speed. Rock X is thrown vertically upward, r

Neko [114]

Answer:

All the three rocks will hit the ground with same speed.

Explanation:

For rocks X and Z, motion is along a straight line but in case of rock Y, motion is two dimensional. Since velocity is a vector it will be difficult for us to calculate the final velocity in each case. So we should find a way to solve this problems using a scalar which is related to velocity. The best and easy to use scalar related to velocity is kinetic energy. Since there is no air resistance, the total mechanical energy of the stone remains the same. Therefore we can use the concept of conservation of mechanical energy to solve this problem.

i.e. initial mechanical energy = final mechanical energy

let us take the edge of the cliff as initial position and ground as the final position.

We know that

Mechanical energy = Kinetic energy + Potential energy

Initial Mechanical energy = Initial Kinetic energy + Initial Potential energy

we know that

Potential energy = mgh

where,

m = mass of the body

g = acceleration due to gravity

h = height from ground

All the three rocks are identical and are thrown from same height. Therefore m and h are same for all the three which implies that the initial potential energy for all the three rocks is same.

Similarly, we know that

Kinetic energy = $\frac{1}{2} mv^{2}$

where,

m = mass of the body

v = velocity of the body

Since all the rocks are thrown with same speed, v is same for all the rocks. Thus initial kinetic energy is also same for all.

Since initial kinetic energy and Initial Potential energy is same for all the three, Initial Mechanical energy is also same for them.

Next let us consider the final position. At the ground h = 0. Therefore final potential energy of all the three rocks is 0. Thus they will be having only kinetic energy.

By conservation of mechanical energy,

initial mechanical energy = final mechanical energy

i.e. Initial Kinetic energy + Initial Potential energy = final Kinetic energy + final Potential energy

final potential energy = 0

thus,

Initial Mechanical energy = Initial Kinetic energy + Initial Potential energy = final Kinetic energy

Initial Mechanical energy = final Kinetic energy

Since Initial Mechanical energy is same for all the three, by the above equation final Kinetic energy is also same for all the three. Since here, kinetic energy is the function of only velocity, final velocity is also same for all the three rocks.

i.e. all the three rocks will hit the ground with same speed.

7 0

4 years ago

An electric current of 200 A is passed through a stainless steel wire having a radius R of 0.001268 m. The wire is L = 0.91 m lo

denis23 [38]

Answer:

The value is $T_m = 435.2 \ K$

Explanation:

From the question we are told that

The current is $I = 200 \ A$

The radius is $R = 0.001268 \ m$

The length of the wire is $L = 0.91 \ m$ \

The resistance is $R = 0.126 \ \Omega$

The outer surface temperature is $T _o = 422.1 \ K$

The average thermal conductivity is $\sigma = 22.5 W/mK$

Generally the heat generated in the stainless steel wire is mathematically represented as

$Q = \frac{Power}{ \pi r^2L}$

$Q = \frac{I^2 R}{ \pi r^2L}$

=> $Q = \frac{200^2 * 0.126}{3.142 * (0.001268)^2 * 0.91}$

=> $Q = 1.096*10^{9}\ W/m^3$

Generally the middle temperature is mathematically represented as

$T_m = T_o + \frac{Q * r^2 }{ 6 * \sigma }$

$T_m = 422.1 + \frac{1.096*10^{-9} * 0.001268^2}{6 * 22.5}$

$T_m = 435.2 \ K$

4 0

3 years ago

the Space Program has benefitted people in everyday life. Describe two ways in which people can benefit

ycow [4]

So we can know what is in space maybe weird or interesting stuff

8 0

3 years ago

Which is not a characteristic of chemical equilibrium?

dimaraw [331]

<span>The answer would be, C. The reactions go to completion</span>

7 0

4 years ago

Read 2 more answers

What is the frequency of an X-ray with wavelength 0.13 nm ? Assume that the wave travels in free space. Express your answer to t

dem82 [27]

Answer:

Frequency, $f=2.30\times 10^{18}\ Hz$

Explanation:

Given that,

The wavelength of the x-rays, $\lambda=0.13\ nm=0.13\times 10^{-9}\ m$

We need to find the frequency of an x-ray. All electromagnetic wave travel with a speed of light. It is given by the formula as :

$c=f\lambda$

f is the frequency

$f=\dfrac{c}{\lambda}\\\\f=\dfrac{3\times 10^8}{0.13\times 10^{-9}}\\\\f=2.30\times 10^{18}\ Hz$

So, the frequency of an x-ray is $2.30\times 10^{18}\ Hz$ . Hence, this is the required solution.

5 0

3 years ago