Please help me!

1) Karen shouts across a canyon and hears an
echo 5.7 s later.
How wide is the canyon? The speed of
sound is 343 m/s.
Answer in units of m.

2) The distance between two consecutive nodes
of a standing wave is 16.8 cm. The hand generating
the pulses moves up and down through
a complete cycle 2.22 times every 7.59 s.
Find the velocity of the wave.
Answer in units of m/s.

Boi Mikayla, your out here putting your own words in your mouth lmao.

1) To find the width of the canyon, we need to use the formula:

Width = (Speed of sound * Time) / 2

Plugging in the given values:

Width = (343 m/s * 5.7 s) / 2

Width = (1955.1 m) / 2

Width = 977.55 m

Therefore, the width of the canyon is 977.55 meters.

2) To find the velocity of the wave, we can use the formula:

Velocity = (Wavelength * Frequency)

First, we need to find the wavelength:

Wavelength = Distance between consecutive nodes

Wavelength = 16.8 cm = 0.168 m

Next, we need to find the frequency:

Frequency = (Number of cycles / Time)

Frequency = 2.22 / 7.59

Frequency = 0.292 cycles/s

Now, we can calculate the velocity of the wave:

Velocity = (0.168 m * 0.292 cycles/s)

Velocity = 0.049056 m/s

Therefore, the velocity of the wave is approximately 0.049056 m/s.

Of course! I can help you with both of these questions. Let's start with the first question.

1) To find the width of the canyon, we need to use the formula:

Distance = Speed × Time

Given that the speed of sound is 343 m/s, and Karen hears the echo 5.7 s later, we can substitute these values into the formula:

Distance = 343 m/s × 5.7 s

Calculating this, we get:

Distance = 1955.1 m

Therefore, the width of the canyon is 1955.1 meters.

Now, let's move on to the second question.

2) To find the velocity of the wave, we can use the formula:

Velocity = Wavelength × Frequency

In this case, we have the distance between two consecutive nodes (wavelength) as 16.8 cm, and we also know the frequency of the hand generating the pulses, which is given as 2.22 times every 7.59 s.

To find the frequency, we can use the formula:

Frequency = number of cycles / time

Substituting the given values into the formula, we have:

Frequency = 2.22 / 7.59 s

Calculating this, we get:

Frequency = 0.292 cycles/s

Now, we can substitute the values of wavelength and frequency into the velocity formula:

Velocity = 16.8 cm × 0.292 cycles/s

However, the wavelength needs to be converted to meters, as the velocity should be in units of m/s. Since 1 meter is equal to 100 cm, the wavelength in meters is:

Wavelength = 16.8 cm / 100 = 0.168 m

Now, we can substitute the values into the velocity formula:

Velocity = 0.168 m × 0.292 cycles/s

Calculating this, we get:

Velocity = 0.049 m/s

Therefore, the velocity of the wave is 0.049 meters per second.

I hope this helps! Let me know if you have any further questions.

1) the sound goes over and back

... 2 w =5.7 * 343

2)velocity = frequency * wavelength
... v = (2.22 / 7.59) * .168 m