Advertisements
Advertisements
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.
Advertisements
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`
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.
APPEARS IN
संबंधित प्रश्न
Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with humidity.
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 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 `(3λ)/4`.
Velocity of sound in air is 332 m s−1. Its velocity in vacuum will be
Two wave pulses travel in opposite directions on a string and approach each other. The shape of one pulse is inverted with respect to the other.
Two waves of equal amplitude A, and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is
A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416. Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to
A pulse travelling on a string is represented by the function \[y = \frac{a^2}{\left( x - \nu t \right)^2 + a^2},\] where a = 5 mm and ν = 20 cm-1. Sketch the shape of the string at t = 0, 1 s and 2 s. Take x = 0 in the middle of the string.
The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is v. Write the wave equation.
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.
The equation of a wave travelling on a string is:
\[y = \left( 0 \cdot 10 \text{ mm } \right) \sin\left[ \left( 31 \cdot 4 m^{- 1} \right)x + \left( 314 s^{- 1} \right)t \right]\]
- In which direction does the wave travel?
- Find the wave speed, the wavelength and the frequency of the wave.
- What is the maximum displacement and the maximum speed of a portion of the string?
A wave travelling on a string at a speed of 10 m s−1 causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave? (b) If the displacement of a particle of 1⋅5 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant?
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.
Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with temperature.
A bat emits an ultrasonic sound of frequency 1000 kHz in the air. If the sound meets a water surface, what is the wavelength of the the reflected sound? The speed of sound in air is 340 m s–1 and in water 1486 m s–1.
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 4 m.
Sound waves of wavelength λ travelling in a medium with a speed of v m/s enter into another medium where its speed is 2v m/s. Wavelength of sound waves in the second medium is ______.
At what temperatures (in °C) will the speed of sound in air be 3 times its value at O°C?
If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.
The displacement y of a particle in a medium can be expressed as, y = `10^-6sin(100t + 20x + pi/4)` m where t is in second and x in meter. The speed of the wave is ______.
