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## Homework Statement

Consider ultrasound with a frequency of 40 kHz.

(a) What is the wavelength and period of a 40 kHz sound wave?

(b) The slit width required to give the first order diffraction minimum at thirty degrees.

(c) Calculate the angles at which the first three minimums should be observed for single slit diffraction with the following slit widths:

1. three and a half times the wavelength:

2. five times the wavelength:

3. twice the wavelength:

## Homework Equations

a sin

*θ*= λ

sin

*θ =*

*λ*/*a*## The Attempt at a Solution

(a)

40kHz = 40,000Hz

v = speed of sound = 343m/s

f = 40,000Hz

f = 1/T

T = 1/f = 1/40,000 = [2.5*10^(-5)]

λ = v/f = 343/40000 = [8.575*10^(-3)nm]

I'm not sure if this is correct.

(b)

__slit width = a__

slit separation = d

angle =

slit separation = d

angle =

*θ*a sin

*θ*= λ

sin

*θ =*

*λ*/*a*sin

*30*= (8.575*10^(-3)) / a

0.5 = (8.575*10^(-3)) / a

a = λ/sin

*30*= [0.01715um]

I am sure that this is wrong.

(c)

I am not sure how to calculate this with the limited variables that I have to work with.