Waves, Sound & Optics
Every waves, sound & optics calculator on CalcEngines — each with its formula, a worked example, the standard it follows and the assumptions it makes.
8 calculators in this section
- Beat Frequency CalculatorTwo close notes do not average into one. They rise and fall at the DIFFERENCE of their frequencies while sounding at the MEAN of them, and below about seven beats a second you can count the throb. This page gives the beat rate, the beat period, the pitch you actually hear and the interval in cents, and says which side of countable you are on.
- Doppler Effect Calculator: Source and Observer MovingMove the source at 30 m/s and you get one answer. Move the observer at 30 m/s instead and you get a different one. The formula is not symmetric and this page prints both so you can see by how much — along with the whole drop as a horn passes you, the wavelength in front and behind, and what happens as the source approaches the speed of sound.
- Optics Sign Convention: Cartesian or Real-Is-PositiveTwo conventions are in print and they give opposite signs for the same mirror: a concave mirror's focal length is negative in one and positive in the other, and a virtual image's distance changes sign too. Name your convention and your quantity and this gives the sign, the formula that goes with it, and one mirror worked both ways.
- Snell’s Law and Critical Angle CalculatorSnell's law bends a ray; the critical angle says when it stops bending and turns back. This gives the refracted angle, the critical angle for that pair of media in that direction, the Brewster angle, the speed of light in each, and it refuses to answer rather than inventing a refracted ray that does not exist. Every angle is in degrees; the arcsine underneath returns radians and the page converts.
- Standing Waves on a String and in Pipes CalculatorA string and an open pipe of the same length sound the same note. Close one end of the pipe and the note drops an octave but the SPACING between its resonances does not change at all. This page gives the nth mode for all three systems, counts its nodes and antinodes, and says which harmonics a closed pipe simply cannot produce.
- Thin Lens and Mirror Formula CalculatorTwo formulae that differ by one sign, and a convention that decides every other sign on the page. This works the lens and the mirror in the Cartesian convention NCERT and most boards use, prints the image distance, the magnification and the image height, and says in words whether the image is real or virtual and which way up.
- Wave Speed, Frequency and Wavelength CalculatorSend a wave into a second medium and one of the three quantities survives unchanged, one is set by the medium and one has no choice but to move. This page takes a frequency and two media and prints both wavelengths, the ratio between them, and the opposite case — helium, where the wavelength is the fixed one and the pitch is what jumps.
- Young’s Double Slit Fringe Width CalculatorNCERT gives the fringe POSITIONS and leaves the fringe width to be read off the spacing. This page does both, converts the three quantities out of the three different units they always arrive in, and answers the question a number alone does not: at this slit separation and this screen distance, is the pattern coarse enough for anyone to see?