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A Hospital Uses an Ultrasonic Scanner to Locate Tumours in a Tissue. What is the Wavelength of Sound in the Tissue in Which the Speed of Sound is 1.7 Km S–1? the Operating Frequency of the Scanner is 4.2 Mhz.

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प्रश्न

A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is 1.7 km s–1? The operating frequency of the scanner is 4.2 MHz.

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उत्तर १

Speed of sound in the tissue, v = 1.7 km/s = 1.7 × 103 m/s

Operating frequency of the scanner, ν = 4.2 MHz = 4.2 × 106 Hz

The wavelength of sound in the tissue is given as:

`lambda = v/v`

`= (1.7 xx 10^3)/(4.2 xx 10^6) = 4.1 xx 10^(-4) m`

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उत्तर २

Here speed of sound => υ = 1.7 km s-1 = 1700 ms-1 and frequency υ= 4.2 MHz = 4.2 x 106 Hz

∴ Wavelength, A = υ/V = 1700/(4.2 x 106) =4.1 x 10-4 m.

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अध्याय 14: Waves - Exercises [पृष्ठ ३८७]

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एनसीईआरटी Physics Part 1 and 2 [English] Class 11
अध्याय 14 Waves
Exercises | Q 7 | पृष्ठ ३८७

संबंधित प्रश्न

You have learnt that a travelling wave in one dimension is represented by a function y= f (x, t)where x and t must appear in the combination x – v t or x + v t, i.e. y = f (x ± v t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave:

(a) `(x – vt )^2`

(b) `log [(x + vt)/x_0]`

(c) `1/(x + vt)`


For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase?


A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10–2 kg and its linear mass density is 4.0 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?


A train, standing in a station-yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with at a speed of 10 m s–1. What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of 10 m s–1? The speed of sound in still air can be taken as 340 m s–1.


Two strings A and B, made of same material, are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed `v_A` and on B with speed `v_B`. The ratio `v_A/v_B` is ______.


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A wave propagates on a string in the positive x-direction at a velocity \[\nu\] \[t =  t_0\] is given by \[g\left( x, t_0 \right) = A  \sin  \left( x/a \right)\]. Write the wave equation for a general time t.


A travelling wave is produced on a long horizontal string by vibrating an end up and down sinusoidally. The amplitude of vibration is 1⋅0 and the displacement becomes zero 200 times per second. The linear mass density of the string is 0⋅10 kg m−1 and it is kept under a tension of 90 N. (a) Find the speed and the wavelength of the wave. (b) Assume that the wave moves in the positive x-direction and at t = 0, the end x = 0 is at its positive extreme position. Write the wave equation. (c) Find the velocity and acceleration of the particle at x = 50 cm at time t = 10 ms.


A wire of length 2⋅00 m is stretched to a tension of 160 N. If the fundamental frequency of vibration is 100 Hz, find its linear mass density.


A 40 cm wire having a mass of 3⋅2 g is stretched between two fixed supports 40⋅05 cm apart. In its fundamental mode, the wire vibrates at 220 Hz. If the area of cross section of the wire is 1⋅0 mm2, find its Young modulus.


A man standing unsymmetrical position between two mountains and fires a gun. He hears the first echo after 1.5 s and the second echo after 2.5 s. If the speed of sound in air is 340 m/s, then the distance between the mountains will be ______ 


Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with temperature.


For the travelling harmonic wave

y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)

Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of `λ/2`.


Speed of sound wave in air ______.


At what temperatures (in °C) will the speed of sound in air be 3 times its value at O°C?


Given below are some functions of x and t to represent the displacement of an elastic wave.

  1. y = 5 cos (4x) sin (20t)
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  3. y = 10 cos [(252 – 250) πt] cos [(252 + 250)πt]
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State which of these represent

  1. a travelling wave along –x direction
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  3. beats
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Given reasons for your answers.


Two perfectly identical wires kept under tension are in unison. When the tension in the wire is increased by 1% then on sounding them together 3 beats are heard in 2 seconds. What is the frequency of each wire?


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