Question

At a temperature of 25C, calculated the wavelength of sound wave (n=20 k Hz) ​

Answer 1

Answer: Our ears are sensitive or can hear frequencies ranging from 20/s to 20,000/s. The speed of sound at the normal comfortable temperature of 25oC is 346m/s. The wavelengths corresponding to these frequencies are (a)17. 3m & 17.

Explanation:

Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in 30.0ºC air. (Assume that the frequency values are accurate to two significant figures.)

Strategy

To find wavelength from frequency, we can use vw = fλ.

Solution

1. Identify knowns. The value for vw, is given by

v

w

=

(

331

m/s

)

√

T

273

K

.

2. Convert the temperature into kelvin and then enter the temperature into the equation

v

w

=

(

331

m/s

)

√

303

K

273

K

=

348.7

m/s

.

3. Solve the relationship between speed and wavelength for λ:

λ

=

v

w

f

.

4. Enter the speed and the minimum frequency to give the maximum wavelength:

λ

max

=

348.7

m/s

20

Hz

=

17

m

.

5. Enter the speed and the maximum frequency to give the minimum wavelength:

λ

min

=

348.7

m/s

20

,

000

Hz

=

0.017

m

=

1.7

cm

.

Discussion

Because the product of f multiplied by λ equals a constant, the smaller f is, the larger λ must be, and vice versa.

Answer 2

The wavelength of sound wave 17.2цm.

Explanation:

λ=$\frac{v}{n}$

$v=344 ms^{-1}$

$n=20MHz$

$=20*10^{6}Hz$

λ$=\frac{344}{20}*10^{6}$

$=17.2*10^{6}m$

$=17.2$цm.

Therefore, the wavelength of sound wave $17.2$цm.