Advertisements
Advertisements
Question
Two submarines are approaching each other in a calm sea. The first submarine travels at a speed of 36 km h−1 and the other at 54 km h−1 relative to the water. The first submarine sends a sound signal (sound waves in water are also called sonar) at a frequency of 2000 Hz. (a) At what frequency is this signal received from the second submarine. At what frequency is this signal received by the first submarine. Take the speed of of the sound wave in water to be 1500 m s−1.
Advertisements
Solution
Given:
Velocity of water v = 1500 m/s
Frequency of sound signal \[f_0\]= 2000 Hz
Velocity of first submarine vs = 36 kmh−1 = \[36 \times \frac{5}{18} \text{ m/s }\]
Velocity of second submarine \[v_0\]= 54 km h−1 = \[54 \times \frac{5}{18}\] m/s = 15 m/s
Frequency received by the first submarine \[\left( f_1 \right)\] is given by:
\[f_1 = \left( \frac{v + v_0}{v - v_s} \right) f_0\]
On substituting the values, we get:
\[f_1 = \left( \frac{1500 + 15}{1500 - 10} \right) \times (2000)\]
\[ = 2034 \text { Hz }\]
(b) Here,
\[f_0 = 2034 Hz\]
Apparent frequency received by second submarine \[\left( f_2 \right)\] is given by :
\[f_2 = \left( \frac{1500 + 10}{1500 - 15} \right) \times (2034)\]
\[ = 2068 \text { Hz }\]
APPEARS IN
RELATED QUESTIONS
Two waves represented by \[y = a\sin\left( \omega t - kx \right)\] and \[y = a\cos\left( \omega t - kx \right)\] \[y = a\cos\left( \omega t - kx \right)\] are superposed. The resultant wave will have an amplitude
The fundamental frequency of a string is proportional to
A wave pulse passing on a string with a speed of 40 cm s−1 in the negative x-direction has its maximum at x = 0 at t = 0. Where will this maximum be located at t = 5 s?
In a stationary wave,
(a) all the particles of the medium vibrate in phase
(b) all the antinodes vibrates in phase
(c) the alternate antinodes vibrate in phase
(d) all the particles between consecutive nodes vibrate in phase.
A wave is described by the equation \[y = \left( 1 \cdot 0 mm \right) \sin \pi\left( \frac{x}{2 \cdot 0 cm} - \frac{t}{0 \cdot 01 s} \right) .\]
(a) Find the time period and the wavelength? (b) Write the equation for the velocity of the particles. Find the speed of the particle at x = 1⋅0 cm at time t = 0⋅01 s. (c) What are the speeds of the particles at x = 3⋅0 cm, 5⋅0 cm and 7⋅0 cm at t = 0⋅01 s?
(d) What are the speeds of the particles at x = 1⋅0 cm at t = 0⋅011, 0⋅012, and 0⋅013 s?
The speed of sound as measured by a student in the laboratory on a winter day is 340 m s−1 when the room temperature is C17°. What speed will be measured by another student repeating the experiment on a day when the room temperature is 32°C?
Find the change in the volume of 1.0 litre kerosene when it is subjected to an extra pressure of 2.0 × 105 N m−2 from the following data. Density of kerosene = 800 kg m−3and speed of sound in kerosene = 1330 ms−1.
Two stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of one of the speakers as shown in figure. Find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = 320 m s−1.
A closed organ pipe can vibrate at a minimum frequency of 500 Hz. Find the length of the tube. Speed of sound in air = 340 m s−1.
A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1000 Hz and 2000 Hz at which the air column in the tube can resonate. Speed of sound in air is 340 m s−1.
An electronically driven loudspeaker is placed near the open end of a resonance column apparatus. The length of air column in the tube is 80 cm. The frequency of the loudspeaker can be varied between 20 Hz and 2 kHz. Find the frequencies at which the column will resonate. Speed of sound in air = 320 m s−1.
A piston is fitted in a cylindrical tube of small cross section with the other end of the tube open. The tube resonates with a tuning fork of frequency 512 Hz. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of 32.0 cm. Calculate the speed of sound in the air of the tube.
Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a wavelength of 32 cm and the other of 32.2 cm. The speed of sound in air is 350 m s−1.
A bullet passes past a person at a speed of 220 m s−1. Find the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person. Speed of sound in air = 330 m s−1.
A small source of sound vibrating at frequency 500 Hz is rotated in a circle of radius 100/π cm at a constant angular speed of 5.0 revolutions per second. A listener situation situates himself in the plane of the circle. Find the minimum and the maximum frequency of the sound observed. Speed of sound in air = 332 m s−1.
A source emitting sound at frequency 4000 Hz, is moving along the Y-axis with a speed of 22 m s−1. A listener is situated on the ground at the position (660 m, 0). Find the frequency of the sound received by the listener at the instant the source crosses the origin. Speed of sound in air = 330 m s−1.
A source emitting a sound of frequency v is placed at a large distance from an observer. The source starts moving towards the observer with a uniform acceleration a. Find the frequency heard by the observer corresponding to the wave emitted just after the source starts. The speed of sound in the medium is v.
Change in temperature of the medium changes ______.
