हिंदी

The string of a guitar is 80 cm long and has a fundamental frequency of 112 Hz. If a guitarist wishes to produce a frequency of 160 Hz, where should the person press the string?

Advertisements
Advertisements

प्रश्न

The string of a guitar is 80 cm long and has a fundamental frequency of 112 Hz. If a guitarist wishes to produce a frequency of 160 Hz, where should the person press the string?

संख्यात्मक
Advertisements

उत्तर

Given: L1 = 80 cm

n1 = 112 Hz

n2 = 160 Hz

According to the law of length:

n1L1 = n2L2

L2 = `(n_1 L_1)/n_2`

= `(112 (80))/160`

= 56 cm

∴ The guitarist must press the string so that the vibrating length becomes 56 cm.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Superposition of Waves - Exercises [पृष्ठ १५७]

APPEARS IN

बालभारती Physics [English] Standard 12 Maharashtra State Board
अध्याय 6 Superposition of Waves
Exercises | Q 24 | पृष्ठ १५७

संबंधित प्रश्न

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


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 transmitted sound? The speed of sound in air is 340 m s–1 and in water 1486 m s–1.


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.


Choose the correct option:

Which of the following equations represents a wave travelling along Y-axis? 


Velocity of sound in air is 332 m s−1. Its velocity in vacuum will be


A wave pulse, travelling on a two-piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to the incident one. If the incident wave has wavelength λ and the transmitted wave λ'


Two waves of equal amplitude A, and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is


Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be


The equation of a wave travelling on a string stretched along the X-axis is given by
\[y = A  e {}^-  \left( \frac{x}{a} + \frac{t}{T} \right)^2  .\]
(a) Write the dimensions of A, a and T. (b) Find the wave speed. (c) In which direction is the wave travelling? (d) Where is the maximum of the pulse located at t = T? At t = 2 T?


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.


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 wave travels along the positive x-direction with a speed of 20 m s−1. The amplitude of the wave is 0⋅20 cm and the wavelength 2⋅0 cm. (a) Write the suitable wave equation which describes this wave. (b) What is the displacement and velocity of the particle at x= 2⋅0 cm at time = 0 according to the wave equation written? Can you get different values of this quantity if the wave equation is written in a different fashion?


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 string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N m−1 and is stretched by 1⋅0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring?


Two long strings A and B, each having linear mass density
\[1 \cdot 2 \times  {10}^{- 2}   kg   m^{- 1}\] , are stretched by different tensions 4⋅8 N and 7⋅5 N respectively and are kept parallel to each other with their left ends at x = 0. Wave pulses are produced on the strings at the left ends at t = 0 on string A and at t = 20 ms on string B. When and where will the pulse on B overtake that on A?


A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m−1 kept under a tension of 60 N. (a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 2⋅0 m long portion of the string.


The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by
\[y = \left( 0 \cdot 4  cm \right)  \sin\left[ \left( 0 \cdot 314  {cm}^{- 1} \right)  x \right]  \cos  \left[ \left( 600\pi  s^{- 1} \right)  t \right]\]
(a) What is the frequency of vibration? (b) What are the positions of the nodes? (c) What is the length of the string? (d) What is the wavelength and the speed of two travelling waves that can interfere to give this vibration?


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.


An organ pipe of length 0.4 m is open at both ends. The speed of sound in the air is 340 m/s. The fundamental frequency is ______ 


What is the interference of sound waves? 


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.


Speed of sound wave in air ______.


A transverse harmonic wave on a string is described by y(x, t) = 3.0 sin (36t + 0.018x + π/4) where x and y are in cm and t is in s. The positive direction of x is from left to right.

  1. The wave is travelling from right to left.
  2. The speed of the wave is 20 m/s.
  3. Frequency of the wave is 5.7 Hz.
  4. The least distance between two successive crests in the wave is 2.5 cm.

Speed of sound waves in a fluid depends upon ______.

  1. directty on density of the medium.
  2. square of Bulk modulus of the medium.
  3. inversly on the square root of density.
  4. directly on the square root of bulk modulus of the medium.

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?


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×