Tag: physics

The engine is moving toward the hill at 15 m/s (54 km/h). The frequency of the echo is f' = f * (v + vs) / (v - vs), where v is speed of sound and vs is speed of engine. f' = 160 * (335 + 15) / (335 - 15) = 160 * 350 / 320 = 175 Hz.

Distance = 1020 m. Total sound distance = 2 × 1020 = 2040 m. If echo is heard after 1.5 s (assuming 11/2 means 1.5), time available for driver approach = (2040/340) - 1.5 = 6 - 1.5 = 4.5 s. Speed = 1020 / 4.5 = 31 m/s (approximately).

Like all waves, sound waves can be reflected. Sound waves suffer reflection from the large obstacles. As a result of reflection of sound wave from a large obstacle, the sound is heard which is named as an echo. Ordinarily echo is not heard as the reflected sound gets merged with the original sound. Certain conditions have to be satisfied to hear an echo distinctly (as a separate sound).
The sensation of any sound persists in our ear for about 0.1 seconds. This is known as the persistence of hearing. If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off.
As the speed of sound is 340 m/s, the distance traveled by sound in 0.1 second is 34 m. This is twice the minimum distance between a source of sound and the reflector. So, if the obstacle is at a distance of 17 m at least, the reflected sound or the echo is heard after 0.1 second, distinctly. 
In the question, the wall is 25 m away from the man and hence, the man will be able to hear the echo distinctly.

The sensation of any sound persists in our ear for about 0.1 seconds. This is known as the persistence of hearing. If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off. 
As the speed of sound in water is 1400 m/s in the question, the distance traveled by sound in 0.1 second is 35 m, which is calculated from the formula 
$Distance\; traveled=velocity\; of\; sound \times time\; taken$. That is, 140 m. This is twice the minimum distance between a source of sound and the reflector. So, if the obstacle is at a distance of 70 m at least, the reflected sound or the echo is heard after 0.1 second, distinctly.

$\displaystyle V _{air}=340m/s, V _{water}=1440m/s$
Echo is the sound that we hear after reflection of sound wave from the reflecting surface.
i.e., total distance travel by sound wave $=2d$
velocity$\displaystyle=\frac{distance}{time}$
$\displaystyle 1440=\frac{2d}{1.5}\Rightarrow d=\frac{1440\times 1.5}{2}=1080.0m=1.08kms$
Hence, option $B$ is the correct answer.

Like all waves, sound waves can be reflected. Sound waves suffer reflection from the large obstacles. As a result of reflection of sound wave from a large obstacle, the sound is heard which is named as an echo. Ordinarily echo is not heard as the reflected sound gets merged with the original sound. Certain conditions have to be satisfied to hear an echo distinctly (as a separate sound).
The sensation of any sound persists in our ear for about 0.1 seconds. This is known as the persistence of hearing. If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off. As the speed of sound is 340 m/s, the distance traveled by sound in 0.1 second is 34 m. This is twice the minimum distance between a source of sound and the reflector. So, if the obstacle is at a distance of 17 m at least, the reflected sound or the echo is heard after 0.1 second, distinctly. 
In this case, the girl is seated in the middle of the park. So, the sound travels through a distance of 6 m up to the girl and then another 6 m up to the building. The total distance is just 12 m which is less than the minimum distance required for the sound to echo. Hence, the echo cannot be heard in this case. 

The sensation of any sound persists in our ear for about 0.1 seconds.  If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off. As the speed of sound is 340 m/s, the distance travelled by sound in 0.1 second is 34 m. This is twice the minimum distance between a source of sound and the reflector. So, if the obstacle is at a distance of 17 m at least, the reflected sound or the echo is heard after 0.1 second, distinctly.

Echo is not heard distinctly, when next beat overlaps with echo simultaneously.
Time per beat $=$ time taken by reflected beat to reach listener.
d being the distance and drum beating at rate of $40$ per minute.
$\dfrac{2d}{v}=\dfrac{60}{40}=\dfrac{3}{2}$
and $\dfrac{2d-80}{v}=1$
Solving we get $d=240m$

An echo is heard when a sound takes minimum of $0.1 \ s$ to reach the observer after getting reflected from the obstacle.
Let the distance between the distance between the source (or observer) and the obstacle be $x$.
Thus distance traveled by sound to hear echo is $2x$.
Speed of sound  $v = 340 \ m/s$
$\therefore$  $2x = vt$
Or  $2x = 340\times 0.1$
$\implies  \ x = 17 \ m$

When sound waves travel in a medium, it gets reflected from the obstacle and we hear the same sound produced even after some time. This reflected sound is known as echo.
Human ear can hear an echo if the reflected sound reaches the ear after at least $0.1 \ s$. If the reflected sound reaches the human ear in less than $0.1\ s$, then we cannot hear the echo.