An underwater sonar system uses mid-wavelength sound waves. These waves of 15 cm in wavelength propagate through seawater with an amplitude of 0.038 nm. Seawater has a density of 1030 kg/m3, and sound through seawater travels at a speed of 1530 m/s.
What is the intensity level IL of these sonar waves?
The way im approaching it:
frequecy=2530/0.15=10200 therefore Period=9.8*10^-5
I= (1530)(1030)(3.8*10^-11)^2(2pi/T)^2
=1*10^-5
IL=10log(1*10^-5/1*10^-12)= 70
Any help would be appreciated
I agree intensity is 1/2 amplitude^2 *angular freq^2*velocity*density
I= 1/2 (3.8E-8)^2*(2PI*1.02E4)^2*(1.53E3)*1030
I get
I=4.67
check that.
You're on the right track, but there are a few errors in your calculation. Let's go through the steps together to find the correct solution.
First, let's calculate the frequency of the sound wave using the equation:
frequency = speed / wavelength
In this case, the speed of sound through seawater is given as 1530 m/s, and the wavelength is 15 cm, which is equal to 0.15 m. Plugging in these values, we get:
frequency = 1530 / 0.15 = 10200 Hz
Next, we can calculate the period of the wave using the formula:
period = 1 / frequency
In this case, the frequency is 10200 Hz, so the period is:
period = 1 / 10200 = 9.8 * 10^-5 seconds
Now, let's calculate the intensity (I) of the sound wave using the equation:
I = (density * amplitude^2 * (2*pi / period)^2) / 2
The density of seawater is given as 1030 kg/m^3, and the amplitude is 0.038 nm, which is equal to 3.8 * 10^-11 m. Plugging in these values along with the period we calculated, we get:
I = (1030 * (3.8 * 10^-11)^2 * (2 * pi / (9.8 * 10^-5))^2) / 2
Evaluating this expression, we find:
I ā 7.05 * 10^-5 W/m^2
Finally, let's calculate the intensity level (IL) of the sound wave using the equation:
IL = 10 * log10(I / Iā)
Where Iā is the reference intensity of 1 * 10^-12 W/m^2.
Plugging in the values, we get:
IL = 10 * log10(7.05 * 10^-5 / (1 * 10^-12))
Evaluating this expression, we find:
IL ā 77.8 dB
So, the correct answer for the intensity level of these sonar waves is approximately 77.8 dB, not 70 dB as you calculated in your approach.