Answer:
0.83 m or 5.57 m
Explanation:
Destructive interference will occur when the distances from the speakers differ by 1/2 wavelength.
The length of 1 cycle of 72.4 Hz is ...
λ = v/f = (343 m/s)/(72.4 Hz) ≈ 4.738 m
So, the distance of the listener from speaker B is ...
3.2 m ± (4.738 m)/2 = {0.83 m, 5.57 m} . . . either of these distances
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The location could be at additional multiples of 4.738 m, but we think not. The sound intensity drops off with the square of the distance from the speaker, so identical sound waves from the speakers will sound quite different at different distances from the speakers. For best interference, the distances need to be as close to the same as possible. That will be at 3.2 m and 5.57 m.
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<em>Comment on the speed of sound</em>
We don't know what speed you are to use for the speed of sound. We have used 343 m/s. Some sources use 340 m/s, which will give a result different by 2 or 3 cm.
<h2>The hiker will go up to 850 m on the hill</h2>
Explanation:
The total energy gained by the hiker = 140 x 4186 J
This energy is consumed in the potential energy acquired , while climbing up the hill.
The potential energy P.E = mass of hiker x acceleration due to gravity x height
Thus
140 x 4186 = 69 x 10 x h
or h = 
= 850 m
If the 20% of the total energy is used
the height h₀ = 
= 170 m
Answer:
630cm/s
Explanation:
In simple harmonic motion, the tangential velocity is expressed mathematically as v = ὦr
ὦ is the angular velocity = 2πf
r is the radius of the disk
f is the frequency
Given the radius of disk = 10cm
frequency = 10Hz
v = 2πfr
v = 2π×10×10
v = 200π
v = 628.32 cm/s
The tangential velocity = 630cm/s ( to 2 significant figures)
Answer:
|v| = 8.7 cm/s
Explanation:
given:
mass m = 4 kg
spring constant k = 1 N/cm = 100 N/m
at time t = 0:
amplitude A = 0.02m
unknown: velocity v at position y = 0.01 m
1. Finding Ф from the initial conditions:
2. Finding time t at position y = 1 cm:
3. Find velocity v at time t from equation 2:
