A string 4.40 m long is held fixed at both ends. If a sharp blow is...

A string 4.40 m long is held fixed at both ends. If a sharp blow is applied to the string at its center, it takes 0.0400 s for the pulses to travel to the ends of the string and return to the middle.

a)What is the lowest standing wave frequency for this string?

b)What is the second lowest standing wave frequency for this string?

Solutions

Expert Solution

(a)

The lowest standing wave frequency(or fundamental frequency) of the string is given by the expression

The velocity of the sound can be deterimed using the kinematic euqation

Now, the acceleration of the pulse can be found using the equation

Hence, the velocity of the sound on the string is given by

Now, the fundamental frequency of the string is

Therefore, the lowest standing wave frequency of the string is 25 Hz.

(b)The second lowest standing wave frequency for this string is equal to th first harmonic.

Therefore, the second lowest standing wave frequency for this string is 50 Hz.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A string of length L = 1 is held fixed at both ends. The string is...

A string of length L = 1 is held fixed at both ends. The string is initially deformed into a shape given by u(x, t = 0) = sin^2(πx) and released. Assume a value of c2 = 1. Find the solution u(x, t) for the vibration of the string by separation of variables.

Consider an elastic string of length L whose ends are held fixed. The string is set...

Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x). Let L = 10 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) f(x) = 16x L , 0 ≤ x ≤ L 4 , 4, L 4 < x < 3L 4 , 16(L − x) L , 3L 4...

. If a string fixed at both ends resonates in its fundamental mode with a frequency...

. If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate?

1. A string is fixed at both ends. If only the length (L) increases, then the...

1. A string is fixed at both ends. If only the length (L) increases, then the fundamental frequency goes: (circle one) up down 2. If only the tension (T) increases, the fundamental goes: (circle one) up down 3. If only the linear mass density increases, the fundamental goes: (circle one) up down 4. The tension (T) in a string fixed across a 1 m length (L) is 400 Newtons, and the linear mass density of the string is 0.01 kg/m....

For a string fixed at both ends with a constant tension, if you double the frequency...

For a string fixed at both ends with a constant tension, if you double the frequency what happens to the wavelength? For a string fixed at both ends with a constant tension, if you triple the harmonic number what happens to the frequency? Consider the 20th harmonic on a string fixed at both ends. Determine the total KE & net force on each node. For a string fixed at both ends, if you quadruple the tension what happens to the...

A taut string of density p and length b is fixed at both ends. At a...

A taut string of density p and length b is fixed at both ends. At a distance 3b/7 from the origin it is pulled up by an amount h, and at a distance 4b/7 it is pulled down by the same amount. Both points are released simultaneously. Describe the motion and the amplitudes of the normal modes (So, which modes are not excited and why not)

A 1.50-m-long wire having a mass of 0.100 kg is fixed at both ends. The tension...

A 1.50-m-long wire having a mass of 0.100 kg is fixed at both ends. The tension in the wire is maintained at 25.0 N. (a) What are the frequencies of the first three allowed modes of vibration? f1 = 6.4549 Hz f2 = 12.9099 Hz f3 = 19.3649 Hz (b) If a node is observed at a point 0.300 m from one end, in what mode and with what frequency is it vibrating? (Select all that apply.) The frequency is...

A point mass M is suspended in the middle of a string whose ends are fixed...

A point mass M is suspended in the middle of a string whose ends are fixed at the same level distance 2ℓ apart; the mass is distance h below the ends of the string. The total mass of the string is m ≪ M. (a) Find the speed of sound waves along the string and (b) the principal frequency of string vibrations on either side of the mass. (c) Do you think this is the smallest vibration frequency in the...

A string with a length of 35 cm is fixed at both ends. Waves travel along...

A string with a length of 35 cm is fixed at both ends. Waves travel along it at a speed of 4 m/s. What is the frequency of its lowest mode of standing waves? At what distance from the end of the string is the first node if the string is vibrating at four times its fundamental frequency?

1. A thin taut string of mass 5.00 g is fixed at both ends and stretched...

1. A thin taut string of mass 5.00 g is fixed at both ends and stretched such that it has two adjacent harmonics of 525 Hz and 630 Hz. The speed of a traveling wave on the string is 168 m/s. a.Determine which harmonic corresponds to the 630 Hz frequency. b.Find the linear mass density of this string. c.Find the tension in the string.

Subjects