Sound waves obey the same frequency/wavelength equation as all periodic travelli

Question

Sound waves obey the same frequency/wavelength equation as all periodic travelling waves: v = f lambda, where v is the speed of sound, f is the frequency in cycles per second (Hz) and lambda is the wavelength. The equation that gives the actual value of the speed of sound in terms of elastic and inertial properties of the medium is v = squareroot B/rho and it is described in Section 16.2 of your text, on page 511 (pay particular attention to Example 16.4 on page 513). (a) Suppose the temperature of the air is 27.0 degree C = 80.6 degree F = 300.15 K. What is the speed of sound at this temperature? (b) Suppose the frequency is f = 440 Hz (orchestral "a"). What is the wavelength of this sound wave in air? (c) Now suppose this same frequency sound wave crosses underwater. The frequency has to stay the same in the water, but the other two quantities in v = f lambda will be different. First find the speed of sound in water, by determining the bulk modulus of water from Equation 11.14, and Table 11.2 on page 351. and using the standard density of water as 1000 kg/m^3. (d) Find the wavelength of sound of frequency f = 440 Hz in water. (e) Find the speed of sound in pure helium at 27.0 degree C = 80.6 degree F = 300.15 K, using Equation 16.10. For helium, the value of M = 4.00 times 10^-3 kg/mol, and the constant gamma = 1.67. Instead of a Reading Quiz on Wednesday, August 10, we will have the second taking of the "Force Concept Inventory" test that you took at the beginning of the term. Get 10 points for simply showing up to take the test, regardless of what score you get.

Explanation / Answer

A) speed of sound in air at a particular temperature in degree Celsius is

V = 331m/s + 0.6 T0 C Where 331 is the speed of sound in air at freezing temperature

V= 331 + 0.6 x 27 = 347.2 m/s

B) wavelength of sound = v/f = 347.2 / 440 = 0.7891 m

C) v= ( B/ p ) 1/2    Where p is the density of water and B is the bulk modulus of water

V= ( 2.2 x 109 N/ m2 / 1000 kg / m3 ) 1/2

V = 1483.2396 m/s

D) wavelength of sound in water = v/ f = 1483.2396 / 440 = 3.3709m

E) speed of sound in helium = (RT / M )1/2  = ( 1.67x8.314x300.15 / 0.004)1/2 = 1020.71m/s

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.