Question

how to solve it ?

.47. The form of a sound wave travelling through air is S(x,t) = S cos (kx + 3000t +の, where x is in meters and t in seconds. What is the shortest time interval that any air molecule takes along the path to move between displacements SS/ and SSm/3? (Ans: 0.23 ms)

0 0
Add a comment Improve this question Transcribed image text
Answer #1

comparing with standard equation

T = 2 pi /3000 seconds

Sm/3 = Sm cos@

cos@ = 1/3

@ = 70.53 deg

similarly

-Sm/3 = Smcos@

@ = 109.47 deg

d@ = 109.47 - 70.53 = 38.94 deg = 0.216pi radians

As in time T, wave covers 2 pi

2 pi / 0.216 pi = 2 pi / 3000 / dt

4.622 = 2.093 x10^-3/ dt

dt = 0.45 s

Add a comment
Know the answer?
Add Answer to:
how to solve it ? .47. The form of a sound wave travelling through air is...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • If the form of a sound wave traveling through air is s(x, t) - (7.0 nm)...

    If the form of a sound wave traveling through air is s(x, t) - (7.0 nm) cos (kx + (3024 rad/s)t + how much time does any given air molecule along the path take to move between

  • A sound wave of the form s = sm cos(kx - ωt + φ) travels at...

    A sound wave of the form s = sm cos(kx - ωt + φ) travels at 343 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.04 m is at its maximum positive displacement of 6.20 nm and air molecule B at x = 2.08 m is at a positive displacement of 2.00 nm. All the molecules between A and B are at intermediate displacements. What is the frequency of the wave?

  • A traveling sound wave through the air is given by s(x,t) = (9.0nm)cos(kx+(1500 r ad s...

    A traveling sound wave through the air is given by s(x,t) = (9.0nm)cos(kx+(1500 r ad s )t +φ). How long would it take for the air molecule to move between +5.0nm and −5.0nm? Hints: • Note that you are dealing with a function of two variables, x and t. Choose convenient values for s,x, and t to first determine φ. • Assign one of the value for s(t) that is given in the problem, and solve for t. (Keep the...

  • Problem 1: A sound wave of the form s = Smax cos(kx - wt+ 0) travels...

    Problem 1: A sound wave of the form s = Smax cos(kx - wt+ 0) travels at 343 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.000 m is at its maximum positive displacement of 6.00 nm and air molecule B at x = 2.070 m is at a positive displacement of 2.00 nm. All the molecules between A and B are at intermediate displacements. (a) What is the wavelength of...

  • how to solve it ? 37. A sinusoidal sound wave is described by the displacement S(x,t)...

    how to solve it ? 37. A sinusoidal sound wave is described by the displacement S(x,t) (2.00x 108) cos (1.25 x - 1850 ), where x is in meters and t is seconds. What is the pressure amplitude of this wave if it is traveling in a material with a bulk modulus of 2.10x 109 N/m2, (Ans: 52.5 Pa)

  • 5. The longitudinal displacements of air molecules in a sound wave are described by: y-32x 10"...

    5. The longitudinal displacements of air molecules in a sound wave are described by: y-32x 10" sin (3x-15000 mn where x is in meters and t is in seconds. (a) By comparing to the general form of the functions describing sound waves in Equation 1.6 and in Exercise 1.4, determine the amplitude of the longitudinal displacements, the angular wave number, the angular frequency, and the phase angle, giving the correct units for each. Find (b) the propagation speed of the...

  • 1. A sinusoidal sound wave moves through a medium and W is described by the displacement...

    1. A sinusoidal sound wave moves through a medium and W is described by the displacement wave function s(x, t) = 2.00 cos (15.7x - 858t) where sis in micrometers, x is in meters, and tis in sec- onds. Find (a) the amplitude, (b) the wavelength, and (c) the speed of this wave. (d) Determine the instanta- neous displacement from equilibrium of the elements of the medium at the position x = 0.050 0 m at 1 = 3.00 ms....

  • 1. A sinusoidal sound wave moves through a medium and W is described by the displacement...

    1. A sinusoidal sound wave moves through a medium and W is described by the displacement wave function s(x, t) = 2.00 cos (15.7x – 8581) where sis in micrometers, x is in meters, and tis in sec- onds. Find (a) the amplitude, (b) the wavelength, and (c) the speed of this wave. (d) Determine the instanta- neous displacement from equilibrium of the elements of the medium at the position x = 0.050 0 m at 1 = 3.00 ms....

  • 4. The variation of pressure in a sound wave is described by the following function p-17...

    4. The variation of pressure in a sound wave is described by the following function p-17 sin (6.50x-1 500t + π/2) Nm? where x is in meters and t is in seconds. (a) By comparing to the general form of the functions describing sound waves in Equation 1.6 and in Exercise 1.4, determine the amplitude of the pressure variations, the angular wave number, the angular frequency and the phase angle, giving the correct units for each. Determine (b) the amplitude...

  • A sound wave traveling through water can be described by the following wave function: (x, t)...

    A sound wave traveling through water can be described by the following wave function: (x, t) = A cos (kx - omega t + pi/3) A = 0.040 m k = 1.11 rad/m omega = 1646.195 rad/s rho_water = 1.0 times 10^3 kg/m^3 a) What is the wavelength of this wave? What is the period of this wave? b) What is the amplitude of this wave? What is the phase of the wave when t = 3.0 s and x...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT