A guitar string is 90 cm long and has a fundamental frequency of 124 H. Where should it be pressed to produce a fundamental frequency of 180 Hz?

A standing wave is formed by two harmonic waves, \({ Y }_{ 1 }=Asin(kx-\varpi t)\)and \({ Y }_{ 2 }=Asin(kx-\varpi t)\)travelling on a string in opposite directioons. Mass density of the string is \(\rho \) and area of cross-section is s. Find the total mechanical energy between two adjacent nodes on the string.

A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. What is the speed of sound in each case? The speed of sound in still air can be taken as 340ms^-1.

One end of a long string of linear mass density 8.0 x 10^-3 kg m^-1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90kg. The pulley end absorbs all the incoming energy so that reflected waves at the end have negligible amplitude. At t=0, the left and (fork end) of the string  x = 0 has zero transverse displacement (y=0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string.

A set of 65 turning forks is so arranged that each gives 3 beats per second with the previous one and the last sounds the octave of first. Find the frequency of first and last forks?

Write basic conditions for formation of stationary waves.

A standing wave is represented by y = 2A sin kx cos ωx. If one of the component waves is y₁ = A sin (ωt - kx), what is the equation of the second component wave?

Show that a function y(x,t) = A sin(kt - ωt)+B cos (kx - ωt) represents a progressive wave. What is the amplitude, wavelength, velocity and initial phase angle of the wave?

Compare the velocities of sound in hydrogen (H₂) and carbon dioxide (CO₂). The ratio (y) of specific heats of H₂ and CO₂ are respectively 1.4 and 1.3.

Find at what temperature the velocity of sound is air will be 1\(\frac{1}{2}\) times the velocity at 11°C. 

Calculate the number of beats heard per second is there are three sources of sound of freqeuencies 400, 401 and 402 of equal intensity sounded together.

Find the velocity of source of sound, when the frequency appears to be (a) double (b) half, the original frequency to a stationary listener.

An open pipe is suddenly closed at one end with the result that the frequency of sound harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. Calculate the fundamental frequency of the open pipe.

Ritesh is a very good flute player but he did not know how he gets the different tanned sound by closing and opening the flute holes. He went to his music teacher in the school and asked him to explain the reason of getting the different tanned sound from the flute player. His music teacher explained that when the air is pushed into the flute player pipe, nodes and antinodes are formed and by closing and opening the holes at different heights, we hear the different tanned sound. Ritesh was happy to hear it.
(i) What values were shown by Ritesh?
(ii) On a certain day, speed of sound in air is 350 m/s. What is the frequency of fundamental note in a closed pipe of length 0.5 m? Also find the frequency of second overtone.