Calculating Energy of a wave if given frequency

Summary

This video tutorial explains how to calculate the energy of a wave using its frequency. The process is straightforward, utilizing the equation E = h × f, where E is the energy, h is Planck's constant, and f is the frequency. The presenter demonstrates this method with a specific frequency value, ensuring accuracy in significant figures and units. The video also emphasizes the importance of correctly applying constants and units to achieve the correct energy value in joules. The presenter briefly introduces a more complex problem involving wavelength, which will be addressed in the next part of the series.

Takeaways

• 😀 The script explains how to calculate the energy of a wave given its frequency.
• 😀 Planck's constant is used in the energy calculation equation: E = h * frequency.
• 😀 The problem provides the frequency value, 2.45 x 10^4 Hz, and asks to find the energy of the wave.
• 😀 The known value of Planck's constant (h) is 6.63 x 10^-34 joule-seconds.
• 😀 The multiplication of Planck's constant by the frequency gives the energy of the wave.
• 😀 Significant figures must be considered when reporting the final result.
• 😀 The result of the calculation is 1.62435 x 10^-29 joules, rounded to 3 significant figures: 1.62 x 10^-29 joules.
• 😀 The cancellation of units, such as Hertz and seconds, leaves joules as the unit of energy.
• 😀 The main takeaway is that to find the energy of a wave, frequency and Planck's constant are the only variables needed.
• 😀 The script stresses that this type of calculation is straightforward, provided the frequency is given.
• 😀 The next problem, which involves wavelength instead of frequency, will be more complex due to an additional step.

Q & A

What is the formula for calculating the energy of a wave?

The formula for calculating the energy of a wave is E = h × ν, where E is the energy, h is Planck's constant, and ν is the frequency of the wave.

What is Planck's constant and its value?

Planck's constant is a fundamental constant used in quantum mechanics, and its value is 6.63 × 10⁻³⁴ joule-seconds (J·s).

What information is needed to calculate the energy of a wave?

To calculate the energy of a wave, you need the frequency of the wave and Planck's constant.

What is the given frequency in this example?

The given frequency in this example is 2.45 × 10⁴ Hz.

What is the result of the energy calculation in this example?

The result of the energy calculation is 1.62 × 10⁻²⁹ joules, rounded to three significant figures.

Why is it important to consider significant figures when calculating energy?

It is important to consider significant figures to ensure that the precision of the result matches the precision of the provided data.

How do the units of Hertz (Hz) and seconds cancel out in the energy calculation?

The units of Hertz (Hz) are equivalent to 1/seconds, so when multiplied by Planck's constant, the seconds unit cancels out, leaving the result in joules.

What step is involved in the calculation process?

The calculation involves substituting the known values of frequency and Planck's constant into the energy formula and performing the multiplication.

What should be done if the energy formula involves more than three significant figures?

If the energy formula results in more than three significant figures, you should round the result to match the required number of significant figures, which in this case is three.

What will be covered next in the video after the frequency-based energy calculation?

The next topic to be covered is the calculation of energy when given the wavelength of the wave, which requires an additional step.