Advertisements
Advertisements
प्रश्न
A violin player riding on a slow train plays a 440 Hz note. Another violin player standing near the track plays the same note. When the two are closed by and the train approaches the person on the ground, he hears 4.0 beats per second. The speed of sound in air = 340 m s−1. (a) Calculate the speed of the train. (b) What beat frequency is heard by the player in the train?
Advertisements
उत्तर
Given:
Frequency of violins \[f_0\]= 440 Hz
Speed of sound in air v = 340 ms−1
Let the velocity of the train (sources) be vs.
(a) Beat heard by the standing man = 4
∴ frequency \[\left( f_1 \right)\]= 440 + 4
= 444 Hz or 436 Hz
Now,
\[f_1 = \left( \frac{340}{340 - v_s} \right) \times f_0\]
On substituting the values, we have:
\[444 = \left( \frac{340 + 0}{340 - v_s} \right) \times 440\]
\[\Rightarrow 444\left( 340 - v_s \right) = 440 \times 340\]
\[\Rightarrow 340 \times \left( 444 - 440 \right) = 440 \times v_s \]
\[ \Rightarrow 340 \times 4 = 440 \times v_s \]
\[ \Rightarrow v_s = 3 . 09 \text { m/s }= 11 \text { km/h }\]
(b) The sitting man will listen to fewer than 4 beats/s.
APPEARS IN
संबंधित प्रश्न
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
Two periodic waves of amplitudes A1 and A2 pass thorough a region. If A1 > A2, the difference in the maximum and minimum resultant amplitude possible is
following Figure shows a wave pulse at t = 0. The pulse moves to the right with a speed of 10 cm s−1. Sketch the shape of the string at t = 1 s, 2 s and 3 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?
Calculate the speed of sound in oxygen from the following data. The mass of 22.4 litre of oxygen at STP (T = 273 K and p = 1.0 × 105 N m−2) is 32 g, the molar heat capacity of oxygen at constant volume is Cv = 2.5 R and that at constant pressure is Cp = 3.5 R.
In Quincke's experiment the sound detected is changed from a maximum to a minimum when the sliding tube is moved through a distance of 2.50 cm. Find the frequency of sound if the speed of sound in air is 340 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 Kundt's tube apparatus has a copper rod of length 1.0 m clamped at 25 cm from one of the ends. The tube contains air in which the speed of sound is 340 m s−1. The powder collects in heaps separated by a distance of 5.0 cm. Find the speed of sound waves in copper.
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 train approaching a platform at a speed of 54 km h−1 sounds a whistle. An observer on the platform finds its frequency to be 1620 Hz. the train passes the platform keeping the whistle on and without slowing down. What frequency will the observer hear after the train has crossed the platform? The speed of sound in air = 332 m s−1.
Figure shows a person standing somewhere in between two identical tuning forks. each vibrating at 512 Hz. If both the tuning forks move towards right a speed of 5.5 m s−1, find the number of beats heard by the listener. Speed of sound in air = 330 m s−1.
Two trains are travelling towards each other both at a speed of 90 km h−1. If one of the trains sounds a whistle at 500 Hz, what will be the apparent frequency heard in the other train? Speed of sound in air = 350 m s−1.
A traffic policeman sounds a whistle to stop a car-driver approaching towards him. The car-driver does not stop and takes the plea in court that because of the Doppler shift, the frequency of the whistle reaching him might have gone beyond the audible limit of 25 kHz and he did not hear it. Experiments showed that the whistle emits a sound with frequency closed to 16 kHz. Assuming that the claim of the driver is true, how fast was he driving the car? Take the speed of sound in air to be 330 m s−1. Is this speed practical with today's technology?
A car moving at 108 km h−1 finds another car in front it going in the same direction at 72 km h−1. The first car sounds a horn that has a dominant frequency of 800 Hz. What will be the apparent frequency heard by the driver in the front car? Speed of sound in air = 330 m s−1.
A wave of frequency 500 Hz is traveling with a speed of 350 m/s. (a) What is the phase difference between two displacements at a certain point at times 1.0 ms apart? (b) what will be the smallest distance between two points which are 45° out of phase at an instant of time?
Two sources of sound are separated by a distance of 4 m. They both emit sound with the same amplitude and frequency (330 Hz), but they are 180° out of phase. At what points between the two sources, will the sound intensity be maximum?
A spring breaks under tension of 10 kg wt.If the string is used to revolve a body of mass 1.2 kg in a horizontal circle. of radius 50 cm, what is the maximum speed with which a body can be revolved?
Two tuning forks having frequencies 320 Hz and 340 Hz are sounded together to produce sound waves. The velocity of sound in air is 340 m/s. Find the difference in wavelength of these waves.
