# Travelling wave derivation#

A student wants to understand how fast a travelling wave described by $$D(x, t) = A\sin(kx - \omega t)$$ is moving and carries out the following derivation.

$$(1) \quad k = m\omega^{2} \textrm{ so } D(x,t) = A\sin(m\omega^{2}x - \omega t)$$

$$(2) \quad D(x,t) = A\sin(\omega(m\omega x - t)) = D\sin\phi$$

$$(3) \quad 0 = \frac{d\phi}{dt}$$

$$(4) \quad 0= m\omega \frac{dx}{dt} - \frac{dt}{dt}$$

$$(5) \quad v = \frac{1}{m\omega}$$

## Part 1#

Something seems to have gone wrong since their final answer for the speed does not have the correct units. Check any box of line that is incorrect or inconsistent with the previous step. Leave the boxes of lines that are correct empty.

Select all the choices that apply.

Note: You will be awarded full marks only if you select all the correct choices, and none of the incorrect choices. Choosing incorrect choices as well as not choosing correct choices will result in deductions.

• Line 1

• Line 2

• Line 3

• Line 4

• Line 5

## Part 2#

Explain the error in any line you have selected as being incorrect.
{"ft_lang_label":"__label__en","ft_lang_prob":0.85995287,"math_prob":0.9992269,"size":1249,"snap":"2022-40-2023-06","text_gpt3_token_len":364,"char_repetition_ratio":0.13012049,"word_repetition_ratio":0.0,"special_character_ratio":0.28903124,"punctuation_ratio":0.06477733,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986579,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-25T13:52:09Z\",\"WARC-Record-ID\":\"<urn:uuid:4ba6f332-a93a-47f9-b64d-986b151db8e2>\",\"Content-Length\":\"151178\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c8166262-a90c-4610-a968-33f2c90203ca>\",\"WARC-Concurrent-To\":\"<urn:uuid:474008af-4663-423f-a23c-f38c09dd6c40>\",\"WARC-IP-Address\":\"69.163.153.95\",\"WARC-Target-URI\":\"https://firas.moosvi.com/oer/physics_bank/content/public/016.Waves/Traveling%20Waves/Travelling_wave_derivation/Travelling_wave_derivation.html\",\"WARC-Payload-Digest\":\"sha1:HBFPPWXOUF3EVW52BIHERMDCGUBKOHYG\",\"WARC-Block-Digest\":\"sha1:BNRI6DZVW5GD6JFU4IZZ672EWGUO7522\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334579.46_warc_CC-MAIN-20220925132046-20220925162046-00182.warc.gz\"}"}