Question

1. the speed of light is 300,000,000 m/s. what is the frequency of microwaves with a wavelength of 0.01 meter?

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1. what is the period of the microwaves in the above question?

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1. the string on a piano that produces an a sharp vibrates with a frequency of 235 hz. if the sound waves produced by this string have a wavelength in air of 1.49 meters, what is the speed of sound in air?

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1. the average wavelength in a series of ocean waves is 15.0 meters. a wave crest arrives at the shore on an average of every 10.0 seconds, so the frequency is 0.100 hz. what is the average speed of the waves?

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Explanation:

(Question 3):

Step1: Recall wave speed formula

$c = \lambda f$
Where $c$ = speed of light, $\lambda$ = wavelength, $f$ = frequency

Step2: Rearrange for frequency

$f = \frac{c}{\lambda}$

Step3: Substitute given values

$c = 300,000,000 \, \text{m/s}$, $\lambda = 0.01 \, \text{m}$
$f = \frac{300000000}{0.01}$

Step4: Calculate the value

$f = 3 \times 10^{10} \, \text{Hz}$

(Question 4):

Step1: Recall period-frequency relation

$T = \frac{1}{f}$
Where $T$ = period, $f$ = frequency from Q3

Step2: Substitute frequency value

$f = 3 \times 10^{10} \, \text{Hz}$
$T = \frac{1}{3 \times 10^{10}}$

Step3: Calculate the value

$T \approx 3.33 \times 10^{-11} \, \text{s}$

(Question 5):

Step1: Recall wave speed formula

$v = \lambda f$
Where $v$ = wave speed, $\lambda$ = wavelength, $f$ = frequency

Step2: Substitute given values

$f = 235 \, \text{Hz}$, $\lambda = 1.49 \, \text{m}$
$v = 1.49 \times 235$

Step3: Calculate the value

$v = 350.15 \, \text{m/s}$

(Question 6):

Step1: Recall wave speed formula

$v = \lambda f$
Where $v$ = wave speed, $\lambda$ = wavelength, $f$ = frequency

Step2: Substitute given values

$f = 0.100 \, \text{Hz}$, $\lambda = 15.0 \, \text{m}$
$v = 15.0 \times 0.100$

Step3: Calculate the value

$v = 1.50 \, \text{m/s}$

Answer:

(Question 3):
$3 \times 10^{10} \, \text{Hz}$

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