Question

Part A: A spherical wave with a wavelength of 4.0 m is emitted from the origin. At one instant of time, the phase at r = 8.0 m is πrad. At that instant, what is the phase at r = 7.5 m ? Express your answer to two significant figures and include the appropriate units.

Part B: What is the phase at r = 9.5 m at the same instant? Express your answer to two significant figures and include the appropriate units.

2. The sound intensity 54.0 m from a wailing tornado siren is 0.140 W/m2 .

Part A: What is the intensity at 1150 mm ? Express your answer with the appropriate units.

Part B: The weakest intensity likely to be heard over background noise is ≈1μW/m2. Estimate the maximum distance at which the siren can be heard.

Express your answer with the appropriate units.

Answer 1

1.

Part A.

According to wave equation, we can define the wave as a function of distance as:

Where k is the wave number and phi is the phase of the wave. If we take a crest, then:

For a phase of pi:

It means that the position of 8m is at 2m of the crest, then for the same wave, the position of 7.5m is located at 1.5m from the crest. Finally:

Part B.

Following the same reasoning of part A, position of 9.5m is located at 3.5 from the crest. Then:

2.

Power of sound remains as constant. Then:

Where the ratio of areas is proportional to square of radius. Then:

Part A.

Since it is nearer than the reference, then the intensity should be higher.

Part B.

From the equation deduced before: