Math phys can i have help 7-10
for 10 answer choices after 6 are
7. 18.4
8. 14.9
9. 12.7
10. 13.5

007. 4. 124.091

008. 9. 0.232679738562091

009. 1. 66.8457608738846

010. 3. 14.2 N

Explanation:

007. Speed of a wave is the product of its wavelength and it frequency.

v = λ f

For a given velocity, the minimum frequency occurs at the maximum wavelength.

For a standing wave, the distance between the nodes (fixed points that don't oscillate) is a multiple of half the wavelength.

L = k/2 λ

The wavelength is a maximum at k=1 (also known as the first harmonic).

L = 1/2 λ

λ = 2L

Substituting and solving for f:

v = 2L f

f = v / (2L)

f = 546 m/s / (2 × 2.2 m)

f = 124.091 Hz

008. The sound travels from the dolphin to the ocean floor, then back to the dolphin.  So it travels a total distance of 2 × 178 m = 356 m.  At a speed of 1530 m/s, the time it takes for the sound to travel this distance is:

t = d / v

t = 356 m / 1530 m/s

t = 0.232679738562091 s

009. Sound intensity in decibels is:

I(db) = 10 log(I / I₀)

where I is the sound intensity (W/m²) and I₀ is the threshold of hearing.

We know that the sound intensity I is proportional to the number of cars per minute.  If we say n is the number of cars per minute, and k is the constant of proportionality, then:

I(db) = 10 log(kn / I₀)

When n = 132, I = 73.

73 = 10 log(132k / I₀)

7.3 = log(132k / I₀)

10^7.3 = 132k / I₀

k / I₀ = (10^7.3) / 132

k / I₀ = 151156.236

So the equation for intensity in decibels is:

I(db) = 10 log(151156.236 n)

When n = 32:

I(db) = 10 log(151156.236 × 32)

I(db) = 66.8457608738846

010. For a vibrating string, the tension is:

T = v² m/L

where v is the speed and m/L is the mass per length of the string.

When v = 18.6, T = 6.43.

6.43 = (18.6)² m/L

m/L = 0.01859

So the equation is:

T = 0.01859 v²

When v = 27.6:

T = 0.01859 (27.6)²

T = 14.2 N

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